43Axx Harmonic analysis on groups and semigroups
This subtopic studies harmonic analysis on groups and semigroups, where Fourier-type methods are adapted to algebraic structures with symmetry and translation invariance.
Specific topics
43A05 Measures on groups and semigroups
Overview
This topic studies measures on groups and semigroups within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A07 Means on groups, semigroups, etc.; amenability
Overview
This topic studies means on groups, semigroups, etc.; amenability within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A10 Measure algebras on groups, semigroups, etc.
Overview
This topic studies measure algebras on groups, semigroups, etc. within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A15 $L^p$-spaces and other function spaces on groups, semigroups, etc.
Overview
This topic studies $l^p$-spaces and other function spaces on groups, semigroups, etc. within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A17 Analysis on ordered groups, $H^p$-theory
Overview
This topic studies analysis on ordered groups, $h^p$-theory within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A20 $L^1$-algebras on groups, semigroups, etc.
Overview
This topic studies $l^1$-algebras on groups, semigroups, etc. within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A22 Homomorphisms and multipliers of function spaces on groups, semigroups, etc.
Overview
This topic studies homomorphisms and multipliers of function spaces on groups, semigroups, etc. within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
Overview
This topic studies fourier and fourier-stieltjes transforms on locally compact and other abelian groups within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A30 Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups
Overview
This topic studies fourier and fourier-stieltjes transforms on nonabelian groups and on semigroups within harmonic analysis on groups and semigroups, emphasizing structural theorems, convergence behavior, and computational implications.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Function-space and operator-theoretic viewpoints
- Convergence, boundedness, and representation properties
- Connections between abstract theory and applied analysis
Typical Uses
Used in research and applications involving harmonic analysis on groups and semigroups, including rigorous analysis of transforms, expansions, and operators.
Applications
- Fourier/harmonic analysis
- Partial differential equations
- Signal and data modeling
References
Recommended Textbooks
43A32 Other transforms and operators of Fourier type
Overview
This topic studies other transforms and operators of fourier type within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A35 Positive definite functions on groups, semigroups, etc.
Overview
This topic studies positive definite functions on groups, semigroups, etc. within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A40 Character groups and dual objects
Overview
This topic studies character groups and dual objects within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A45 Spectral synthesis on groups, semigroups, etc.
Overview
This topic studies spectral synthesis on groups, semigroups, etc. within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A46 Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.)
Overview
This topic studies special sets (thin sets, kronecker sets, helson sets, ditkin sets, sidon sets, etc.) within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A50 Convergence of Fourier series and of inverse transforms
Overview
This topic studies convergence of fourier series and of inverse transforms within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A55 Summability methods on groups, semigroups, etc.
Overview
This topic studies summability methods on groups, semigroups, etc. within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A60 Almost periodic functions on groups and semigroups and their generalizations
Overview
This topic studies almost periodic functions on groups and semigroups and their generalizations within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A62 Harmonic analysis on hypergroups
Overview
This topic studies harmonic analysis on hypergroups within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A65 Representations of groups, semigroups, etc.
Overview
This topic studies representations of groups, semigroups, etc. within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A70 Analysis on specific locally compact and other abelian groups
Overview
This topic studies analysis on specific locally compact and other abelian groups within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A75 Harmonic analysis on specific compact groups
Overview
This topic studies harmonic analysis on specific compact groups within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A77 Harmonic analysis on general compact groups
Overview
This topic studies harmonic analysis on general compact groups within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A80 Analysis on other specific Lie groups
Overview
This topic studies analysis on other specific lie groups within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A85 Harmonic analysis on homogeneous spaces
Overview
This topic studies harmonic analysis on homogeneous spaces within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A90 Spherical functions, Gelfand pairs; spherical harmonics
Overview
This topic studies spherical functions, gelfand pairs; spherical harmonics within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A95 Categorical methods for abstract harmonic analysis
Overview
This topic studies categorical methods for abstract harmonic analysis within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks
43A99 None of the above
Overview
This topic studies none of the above within harmonic analysis on groups and semigroups, with emphasis on theoretical foundations, operator behavior, and practical analytical techniques.
Related Wikipedia Page
Harmonic analysis on topological groups (Wikipedia)
Useful Links
Key Ideas
- Structural characterization of transforms, operators, or function classes
- Convergence and boundedness criteria in relevant function spaces
- Links between abstract theory and concrete analytic problems
Typical Uses
Used to analyze and solve problems in harmonic analysis on groups and semigroups, including representation, inversion, and stability questions.
Applications
- Harmonic and functional analysis
- Partial differential equations
- Signal and systems analysis
References
Recommended Textbooks