Operator Methods in Mathematical Physics
Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland
1st Edition
Published on 8. January 2013
IX, 178 pages
978-3-0348-0531-5 (ISBN)
Description
The conference Operator Theory, Analysis and Mathematical Physics - OTAMP is a regular biennial event devoted to mathematical problems on the border between analysis and mathematical physics. The current volume presents articles written by participants, mostly invited speakers, and is devoted to problems at the forefront of modern mathematical physics such as spectral properties of CMV matrices and inverse problems for the non-classical Schrödinger equation. Other contributions deal with equations from mathematical physics and study their properties using methods of spectral analysis. The volume explores several new directions of research and may serve as a source of new ideas and problems for all scientists interested in modern mathematical physics.
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Jan Janas | Pavel Kurasov | A. Laptev
Operator Methods in Mathematical Physics
Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland
Book
06/2015
Birkhäuser
€106.99
Shipment within 10-15 days
Jan Janas | Pavel Kurasov | A. Laptev
Operator Methods in Mathematical Physics
Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland
Book
01/2013
1st Edition
Birkhäuser
€106.99
Shipment within 10-15 days
Content
- Intro
- Operators Methods in Mathematical Physics
- Conference on Operator Theory, Analysis and Mathematical Physics (OTAMP) 2010, Bedlewo, Poland
- Contents
- Introduction
- Inverse Scattering for Non-classical Impedance Schrödinger Operators
- 1. Introduction
- 1.1. Basic definitions
- 1.2. Miura potentials: the case of absolutely continuous p
- 1.3. A physical example with discontinuous impedance
- 1.4. Some singular impedance Schr¨odinger operators not discussed
- 2. The general approach and main results
- 2.1. The continuous case
- 2.2. The discrete case
- 3. Inverse scattering for Miura potentials
- 3.1. Jost solutions
- 3.2. The scattering data
- 3.3. Reconstruction of the transmission coefficient
- 3.4. The inverse problem
- 3.5. Sobolev properties of the scattering mappings
- 4. The case of discontinuous impedance function
- 4.1. The operators
- 4.2. Jost solutions and the scattering data
- 4.3. Transformation operators
- 4.4. Derivation of the Marchenko equation
- 4.5. Derivation of the Zakharov-Shabat system
- 4.6. Solution of the Zakharov-Shabat system
- 4.7. The inverse scattering problem
- 4.8. Some generalizations
- Appendix
- Acknowledgement
- References
- Finite and Infinite Gap Jacobi Matrices
- 1. Introduction
- 2. Perturbations of the free Jacobi matrix
- 3. Finite gap Jacobi matrices
- 4. Infinite gap Jacobi matrices
- References
- Derivation of Ginzburg-Landau Theory for a One-dimensional System with Contact Interaction
- 1. Introduction and main results
- 1.1. Introduction
- 1.2. The BCS functional
- 1.2.1. The translation-invariant case
- 1.3. The GL functional
- 1.4. Main results
- 1.5. The coefficients in the GL functional
- 2. Sketch of the proof
- 3. Semiclassics
- 4. Upper bound
- 5. Lower bound
- 5.1. The relative entropy
- 5.2. A priori estimates on a
- 5.3. Decomposition of a
- 5.4. The lower bound
- 6. Proof of semiclassical asymptotics
- 6.1. Preliminaries
- 6.2. Proof of Theorem 3.1
- 6.3. Proof of Theorem 3.2
- Acknowledgment
- References
- Eigenfunction Expansions Associated with the One-dimensional Schrödinger Operator
- 1. Introduction
- 2. Mathematical background
- 3. Diagonalising the spectral density matrix
- 4. The case of simple spectrum
- Acknowledgement
- References
- Spectral Minimal Partitions for a Thin Strip on a Cylinder or a Thin Annulus like Domain with Neumann Condition
- 1. Introduction
- 2. Neumann problem for a strip on the cylinder
- 3. Extension to minimal k-partitions of C(b)
- 4. Generalization to other thin domains
- Acknowledgement
- References
- Jacobi and CMV Matrices with Coefficients of Generalized Bounded Variation
- Acknowledgement
- References
- Order Convergence Ergodic Theorems in Rearrangement Invariant Spaces
- 1. Introduction
- 2. Main results
- 3. Dominated Ergodic Theorem
- 4. Converse Dominated Ergodic Theorem
- 5. Pointwise Ergodic Theorem
- 6. Consequences for Orlicz and Lorentz spaces
- Orlicz spaces
- Zygmund classes
- Lorentz spaces
- 7. Additional comments and remarks
- Orlicz-Lorentz spaces
- Order convergence of conditional expectations
- OET on finite measure spaces
- Convergence in norm
- References
- Local Approximation of Observables and Commutator Bounds
- 1. Introduction
- 2. The main lemma
- 3. Application to infinite systems
- 4. Extension to general von Neumann algebras
- Acknowledgment
- References
- The Spectra of Selfadjoint Extensions of Entire Operators with Deficiency Indices (1,1)
- 1. Introduction
- 2. On symmetric operators with not necessarily dense domain
- 3. A review on de Branges spaces with zero-free functions
- 4. A functional model for operators in S(H)
- 5. Spectral characterization
- 6. Concluding remarks
- Acknowledgment
- References
- Asymptotics of Eigenvalues of an Energy Operator in a Problem of Quantum Physics
- 1. Introduction and main results
- 2. Selection of the main component in the asymptotics
- 3. Estimation of the remainder
- Acknowledgment
- References
