The Resource PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann
PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann
Resource Information
The item PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in socalled PTsymmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PTsymmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all  provided one is familiar with the theory of selfadjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of selfadjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively formbounded perturbations and for pseudoFriedrichs extensions. The author pays particular attention to the case when the unperturbed selfadjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum
 Language
 eng
 Extent
 1 online resource
 Contents

 Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of SelfAdjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces
 Chapter 2 Relatively FormBoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively FormBounded and Relatively FormCompact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; 2.3 PseudoFriedrichs Extensions; 2.3.1 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
 Isbn
 9783834817624
 Label
 PTsymmetric Schrödinger operators with unbounded potentials
 Title
 PTsymmetric Schrödinger operators with unbounded potentials
 Statement of responsibility
 Jan Nesemann
 Language
 eng
 Summary
 Following the pioneering work of Carl M. Bender et al. (1998), there has been an increasing interest in theoretical physics in socalled PTsymmetric Schrödinger operators. In the physical literature, the existence of Schrödinger operators with PTsymmetric complex potentials having real spectrum was considered a surprise and many examples of such potentials were studied in the sequel. From a mathematical point of view, however, this is no surprise at all  provided one is familiar with the theory of selfadjoint operators in Krein spaces. Jan Nesemann studies relatively bounded perturbations of selfadjoint operators in Krein spaces with real spectrum. The main results provide conditions which guarantee the spectrum of the perturbed operator to remain real. Similar results are established for relatively formbounded perturbations and for pseudoFriedrichs extensions. The author pays particular attention to the case when the unperturbed selfadjoint operator has infinitely many spectral gaps, either between eigenvalues or, more generally, between separated parts of the spectrum
 Cataloging source
 HKP
 http://library.link/vocab/creatorName
 Nesemann, Jan
 Dewey number
 510
 Index
 no index present
 Language note
 English
 LC call number
 QA329
 LC item number
 .N47 2011eb
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/subjectName

 Operator theory
 Kreĭn spaces
 Kreĭn spaces
 Operator theory
 Label
 PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of SelfAdjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces
 Chapter 2 Relatively FormBoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively FormBounded and Relatively FormCompact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; 2.3 PseudoFriedrichs Extensions; 2.3.1 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
 Control code
 756192733
 Dimensions
 unknown
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9783834817624
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783834883278
 Specific material designation
 remote
 System control number
 (OCoLC)756192733
 Label
 PTsymmetric Schrödinger operators with unbounded potentials, Jan Nesemann
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 mixed
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Acknowledgment; Table of Contents; Introduction; Chapter 1 Relatively Bounded Perturbations inKrein Spaces; 1.1 Linear Operators in Krein Spaces; 1.2 Stability Theorems; 1.2.1 Relatively Bounded and Relatively CompactOperators; 1.2.2 The Case of Relative Bound 0; 1.2.3 Stability of SelfAdjointness in Krein Spaces; 1.3 Continuity of Separated Parts of the Spectrum; 1.3.1 Continuity of Resolvents; 1.3.2 Perturbation of Isolated Parts of the Spectrum; 1.3.3 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 1.3.4 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces
 Chapter 2 Relatively FormBoundedPerturbations in Krein Spaces2.1 Stability Theorems; 2.1.1 Accretive and Sectorial Operators; 2.1.2 Quadratic Forms and Associated Operators; 2.1.3 Relatively FormBounded and Relatively FormCompact Operators; 2.2 Continuity of Separated Parts of the Spectrum; 2.2.1 Perturbation of Spectra of SelfAdjoint Operatorsin Hilbert Spaces; 2.2.2 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; 2.3 PseudoFriedrichs Extensions; 2.3.1 Perturbation of Spectra of SelfAdjoint Operatorsin Krein Spaces; Chapter 3Examples; 3.1 Example 1; 3.2 Example 2
 Control code
 756192733
 Dimensions
 unknown
 Extent
 1 online resource
 Form of item
 online
 Isbn
 9783834817624
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783834883278
 Specific material designation
 remote
 System control number
 (OCoLC)756192733
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