34Lxx Ordinary differential operators and spectral theory
This subtopic studies ordinary differential operators and spectral theory, connecting operator methods with eigenvalues, eigenfunctions, and boundary problems.
Specific topics
34L05 General spectral theory of ordinary differential operators
Overview
34L05 studies general spectral theory of ordinary differential operators in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general spectral theory of ordinary differential operators
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L10 Eigenfunctions, eigenfunction expansions, completeness
Overview
34L10 studies eigenfunctions, eigenfunction expansions, completeness in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for eigenfunctions, eigenfunction expansions, completeness
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds for ordinary differential operators
Overview
34L15 studies eigenvalues, estimation of eigenvalues, upper and lower bounds for ordinary differential operators in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for eigenvalues, estimation of eigenvalues, upper and lower bounds for ordinary differential operators
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum
Overview
34L16 studies numerical approximation of eigenvalues and of other parts of the spectrum in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for numerical approximation of eigenvalues and of other parts of the spectrum
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
Overview
34L20 studies asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L25 Scattering theory, inverse scattering
Overview
34L25 studies scattering theory, inverse scattering in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for scattering theory, inverse scattering
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L30 Nonlinear ordinary differential operators
Overview
34L30 studies nonlinear ordinary differential operators in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nonlinear ordinary differential operators
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
Overview
34L40 studies particular ordinary differential operators (dirac, one-dimensional schrã¶dinger, etc.) in ordinary differential operators and spectral theory. It studies differential operators defined by ODEs and their spectral properties, including eigenvalues and eigenfunctions.
Related Wikipedia Page
Ordinary Differential Operators And Spectral Theory (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for particular ordinary differential operators (dirac, one-dimensional schrã¶dinger, etc.)
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in mathematical physics and spectral analysis of boundary problems.
Applications
- Sturm-Liouville operators
- Eigenvalue problems
- Quantum and wave models
References
Recommended Textbooks