32Axx Holomorphic functions
This subtopic studies holomorphic functions, covering core complex analytic properties, local behavior, and global function-theoretic phenomena.
Specific topics
32A05 Power series, series of functions of several complex variables
Overview
32A05 studies power series, series of functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for power series, series of functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A07 Special domains in $\mathbb{C}^n$
Overview
32A07 studies special domains in $\mathbb{c}^n$ in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special domains in $\mathbb{c}^n$
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A10 Holomorphic functions of several complex variables
Overview
32A10 studies holomorphic functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for holomorphic functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A12 Multifunctions of several complex variables
Overview
32A12 studies multifunctions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for multifunctions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A15 Entire functions of several complex variables
Overview
32A15 studies entire functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for entire functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A17 Special families of functions of several complex variables
Overview
32A17 studies special families of functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special families of functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A18 Bloch functions, normal functions of several complex variables
Overview
32A18 studies bloch functions, normal functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for bloch functions, normal functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A19 Normal families of functions, normal classes
Overview
32A19 studies normal families of functions, normal classes in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for normal families of functions, normal classes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A20 Meromorphic functions of several complex variables
Overview
32A20 studies meromorphic functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for meromorphic functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A22 Nevanlinna theory; growth estimates; other inequalities
Overview
32A22 studies nevanlinna theory; growth estimates; other inequalities in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nevanlinna theory; growth estimates; other inequalities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A25 Integral representations; canonical kernels
Overview
32A25 studies integral representations; canonical kernels in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral representations; canonical kernels
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A26 Integral representations, constructed kernels
Overview
32A26 studies integral representations, constructed kernels in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral representations, constructed kernels
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A27 Cauchy-Stieltjes type integrals
Overview
32A27 studies cauchy-stieltjes type integrals in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for cauchy-stieltjes type integrals
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A30 Other generalizations of function theory of one complex variable
Overview
32A30 studies other generalizations of function theory of one complex variable in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other generalizations of function theory of one complex variable
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A35 $H^p$-spaces, Nevanlinna spaces of functions in several complex variables
Overview
32A35 studies $h^p$-spaces, nevanlinna spaces of functions in several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for $h^p$-spaces, nevanlinna spaces of functions in several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A36 Bergman spaces of functions in several complex variables
Overview
32A36 studies bergman spaces of functions in several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for bergman spaces of functions in several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A37 Other spaces of holomorphic functions
Overview
32A37 studies other spaces of holomorphic functions in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for other spaces of holomorphic functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A38 Algebras of holomorphic functions of several complex variables
Overview
32A38 studies algebras of holomorphic functions of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for algebras of holomorphic functions of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A40 Boundary behavior of holomorphic functions
Overview
32A40 studies boundary behavior of holomorphic functions in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for boundary behavior of holomorphic functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A45 Hyperfunctions
Overview
32A45 studies hyperfunctions in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for hyperfunctions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A50 Harmonic analysis of several complex variables
Overview
32A50 studies harmonic analysis of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for harmonic analysis of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A55 Singular integrals of several complex variables
Overview
32A55 studies singular integrals of several complex variables in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for singular integrals of several complex variables
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks
32A60 Zero sets of holomorphic functions
Overview
32A60 studies zero sets of holomorphic functions in holomorphic functions. It studies holomorphic functions of one complex variable, including local analyticity, mapping behavior, and boundary regularity.
Related Wikipedia Page
Holomorphic Functions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for zero sets of holomorphic functions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used as the base theory for classical complex analysis.
Applications
- Analyticity and Cauchy theory
- Conformal mapping
- Complex-variable approximation
References
Recommended Textbooks