Ebook: Spectral Methods for Operators of Mathematical Physics

This book presents recent results from the following areas: spectral analysis of one-dimensional Schrödinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

---

This book presents recent results from the following areas: spectral analysis of one-dimensional Schr?dinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

---

This book presents recent results from the following areas: spectral analysis of one-dimensional Schr?dinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Content:
Front Matter....Pages i-viii
Partial Non-stationary Perturbation Determinants....Pages 1-18
Noncommuting Domination....Pages 19-33
The Problem of the Finiteness of the Point Spectrum for Self-adjoint Operators. Perturbations of Wiener-Hopf Operators and Applications to Jacobi Matrices....Pages 35-50
Singular Perturbations as Range Perturbations in a Pontryagin Space....Pages 51-68
Minimal Realizations of Scalar Generalized Nevanlinna Functions Related to Their Basic Factorization....Pages 69-90
Eigenvalues and Spectral Gaps Related to Periodic Perturbations of Jacobi Matrices....Pages 91-100
WKB and Turning Point Theory for Second-order Difference Equations....Pages 101-138
Bounds for the Points of Spectral Concentration of One-dimensional Schr?dinger Operators....Pages 139-149
Reconstructing Jacobi Matrices from Three Spectra....Pages 151-154
On Some Asymptotic Properties of Solutions for a Particular Class of Finite Difference Equations....Pages 155-162
A Remark on Spectral Meaning of the Symmetric Functional Model....Pages 163-177
A Remark on Equivalence of Weak and Strong Definitions of the Absolutely Continuous Subspace for Nonself-adjoint Operators....Pages 179-184
On a Transformation of the Sturm-Liouville Equation with Slowly Decaying Potentials and the Titchmarsh-Weyl m-function....Pages 185-201
Uniform Levinson Type Theorems for Discrete Linear Systems....Pages 203-218
Free Functional Model Related to Simply-connected Domains....Pages 219-231
Jacobi Block Matrices with Constant Matrix Terms....Pages 233-238
Back Matter....Pages 239-244

---

This book presents recent results from the following areas: spectral analysis of one-dimensional Schr?dinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators. It is addressed to a wide group of specialists working in operator theory or mathematical physics.

Content:
Front Matter....Pages i-viii
Partial Non-stationary Perturbation Determinants....Pages 1-18
Noncommuting Domination....Pages 19-33
The Problem of the Finiteness of the Point Spectrum for Self-adjoint Operators. Perturbations of Wiener-Hopf Operators and Applications to Jacobi Matrices....Pages 35-50
Singular Perturbations as Range Perturbations in a Pontryagin Space....Pages 51-68
Minimal Realizations of Scalar Generalized Nevanlinna Functions Related to Their Basic Factorization....Pages 69-90
Eigenvalues and Spectral Gaps Related to Periodic Perturbations of Jacobi Matrices....Pages 91-100
WKB and Turning Point Theory for Second-order Difference Equations....Pages 101-138
Bounds for the Points of Spectral Concentration of One-dimensional Schr?dinger Operators....Pages 139-149
Reconstructing Jacobi Matrices from Three Spectra....Pages 151-154
On Some Asymptotic Properties of Solutions for a Particular Class of Finite Difference Equations....Pages 155-162
A Remark on Spectral Meaning of the Symmetric Functional Model....Pages 163-177
A Remark on Equivalence of Weak and Strong Definitions of the Absolutely Continuous Subspace for Nonself-adjoint Operators....Pages 179-184
On a Transformation of the Sturm-Liouville Equation with Slowly Decaying Potentials and the Titchmarsh-Weyl m-function....Pages 185-201
Uniform Levinson Type Theorems for Discrete Linear Systems....Pages 203-218
Free Functional Model Related to Simply-connected Domains....Pages 219-231
Jacobi Block Matrices with Constant Matrix Terms....Pages 233-238
Back Matter....Pages 239-244
....