Perspectives on general left-definite theory

DOI10.1007/978-3-030-75425-9_6zbMath1496.47040arXiv2012.01014OpenAlexW3108169956MaRDI QIDQ2066109

Dale Frymark, Constanze Liaw

Publication date: 13 January 2022

Full work available at URL: https://arxiv.org/abs/2012.01014

zbMATH Keywords

spectral theorySturm-Liouville operatorsself-adjoint extensionsfinite rank perturbationsleft-definite theoryBirman-Krein-Vishik theory

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Linear symmetric and selfadjoint operators (unbounded) (47B25) Research exposition (monographs, survey articles) pertaining to operator theory (47-02) Lists of open problems (00A27)

Uses Software

• SLEIGN2

Cites Work

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• On the spectra of left-definite operators
• Some representation theorems for sesquilinear forms
• Glazman-Krein-Naimark theory, left-definite theory and the square of the Legendre polynomials differential operator
• Hilbert scales and Sobolev spaces defined by associated Legendre functions
• Boundary triples and Weyl \(m\)-functions for powers of the Jacobi differential operator
• High order singular rank one perturbations of a positive operator
• Left-definite theory with applications to orthogonal polynomials
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• Boundary conditions associated with the general left-definite theory for differential operators
• A Kato's second type representation theorem for solvable sesquilinear forms
• Perturbation theory for linear operators.
• \({\mathcal H}_{-n}\)-perturbations of self-adjoint operators and Krein's resolvent formula
• The Friedrichs extension of singular differential operators
• Matrix measures and finite rank perturbations of self-adjoint operators
• Properties and decompositions of domains for powers of the Jacobi differential operator
• Spectral analysis, model theory and applications of finite-rank perturbations
• Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression
• Maximal sectorial extensions and closed forms associated with them
• Singular Integrals, Rank One Perturbations and Clark Model in General Situation
• Boundary Value Problems, Weyl Functions, and Differential Operators
• Quasi boundary triples and semi-bounded self-adjoint extensions
• Algorithm 810: The SLEIGN2 Sturm-Liouville Code
• SCALES OF BANACH SPACES

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