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1. The Heat Kernel Lefschetz Fixed Point Formula for the Spin-c Dirac Operator
by J. J. Duistermaat
出版情報: Boston, MA : Springer Science+Business Media, LLC, 2011
シリーズ名: Modern Birkhäuser Classics ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-8247-7
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2. Symplectic Methods in Harmonic Analysis and in Mathematical Physics
by Maurice A. Gosson
出版情報: Basel : Springer Basel AG, 2011
シリーズ名: Pseudo-Differential Operators, Theory and Applications ; 7
オンライン: http://dx.doi.org/10.1007/978-3-7643-9992-4
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3. Self-adjoint Extensions in Quantum Mechanics : General Theory and Applications to Schrödinger and Dirac Equations with Singular Potentials
by D.M. Gitman, I.V. Tyutin, B.L. Voronov
出版情報: Boston : Birkhäuser Boston, 2012
シリーズ名: Progress in Mathematical Physics ; 62
オンライン: http://dx.doi.org/10.1007/978-0-8176-4662-2
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4. Unbounded Self-adjoint Operators on Hilbert Space
by Konrad Schmüdgen
出版情報: Dordrecht : Springer Netherlands : Imprint: Springer, 2012
シリーズ名: Graduate Texts in Mathematics ; 265
オンライン: http://dx.doi.org/10.1007/978-94-007-4753-1
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目次情報: 続きを見る
I Basics onClosed Operators
1 Closed Operators and Adjoint Operators
2 Spectrum of Closed Operators
3 Some Classes of Unbounded Operators
II Spectral Theory
4 Spectral Measures and Spectral Integrals
5 Spectral Decomposition of Selfadjoint and Normal Operators
III Special Topics
6 One-Parameter Groups and Semigroups of Operators
7 Miscellaneous
IV Petirbations of Selfadjointness and of Spectra of Selfadjoint Operators
8 Perturbations of Selfadjoint Operators
9 Trace Class Perturbations of Spectra of Selfadjoint Operators
V Forms and Operators
10 Semibounded Forms and Selfadjoint Operators
11 Sectorial Forms and m-Sectorial Operators
12 Discrete Spectrum of Selfadjoint Operators
VI Selfadjoint Extention Theory of Symmetric Operators
13 Selfajoint Extensions: Cayley Transform and Krein Transform
14 Selfadjoint Extensions: Boundary Triplets
15 Sturm-Liouville Operators
One-Dimensional Moment Problem
I Basics onClosed Operators
1 Closed Operators and Adjoint Operators
2 Spectrum of Closed Operators
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5. Spectral Theory and Applications of Linear Operators and Block Operator Matrices
by Aref Jeribi
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
オンライン: http://dx.doi.org/10.1007/978-3-319-17566-9
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目次情報: 続きを見る
 Introduction
Fredholm Operators and Riesz Theory
Abstract Cauchy Problem
Fredholm Theory Related to Some Measures
 Pertubation Results
Essential Spectra of Linear Operators
Essentia Pseudo-spectra
S-Essential Spectra
Essential Spectra of 2 X 2 Block Operator Matrices
Essential Spectra of 3 X 3 Block Operator Matrices
Applications in Mathematical Physics and Biology.
 Introduction
Fredholm Operators and Riesz Theory
Abstract Cauchy Problem
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6. Evolutionary Equations with Applications in Natural Sciences
edited by Jacek Banasiak, Mustapha Mokhtar-Kharroubi
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2015
シリーズ名: Lecture Notes in Mathematics ; 2126
オンライン: http://dx.doi.org/10.1007/978-3-319-11322-7
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Wilson Lamb: Applying functional analytic techniques to evolution equations
Adam Bobrowski: Boundary conditions in evolutionary equations in biology.-Ernesto Estrada: Introduction to Complex Networks: Structure and Dynamics.-Jacek Banasiak: Kinetic models in natural sciences
Philippe Laurençot: Weak compactness techniques and coagulation equations
Ryszard Rudnicki: Stochastic operators and semigroups and their applications in physics and biology
Mustapha Mokhtar-Kharroubi: Spectral theory for neutron transport.-Anna Marciniak-Czochra: Reaction-diffusion-ODE models of pattern formation
Mapundi Kondwani Banda: Nonlinear Hyperbolic Systems of Conservation Laws and Related Applications
Wilson Lamb: Applying functional analytic techniques to evolution equations
Adam Bobrowski: Boundary conditions in evolutionary equations in biology.-Ernesto Estrada: Introduction to Complex Networks: Structure and Dynamics.-Jacek Banasiak: Kinetic models in natural sciences
Philippe Laurençot: Weak compactness techniques and coagulation equations
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7. The Weyl Operator and its Generalization
by Leon Cohen
出版情報: Basel : Springer Basel : Imprint: Birkhäuser, 2013
シリーズ名: Pseudo-Differential Operators, Theory and Applications ; 9
オンライン: http://dx.doi.org/10.1007/978-3-0348-0294-9
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目次情報: 続きを見る
Introduction
The Fundamental Idea, Terminology, and Operator Algebra
The Weyl Operator
The Algebra of the Weyl Operator
Product of Operators, Commutators, and the Moyal Sin Bracket
Some Other Ordering Rules
Generalized Operator Association
The Fourier, Monomial, and Delta Function Associations
Transformation Between Associations
Path Integral Approach
The Distribution of a Symbol and Operator
The Uncertainty Principle
Phase-Space Distributions
Amplitude, Phase, Instantaneous Frequency, and the Hilbert Transform
Time - Frequency Analysis
The Transformation of Differential Equations into Phase Space
The Representation of Functions
The N Operator Case
Introduction
The Fundamental Idea, Terminology, and Operator Algebra
The Weyl Operator
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8. Analysis as a Tool in Mathematical Physics : In Memory of Boris Pavlov. 1st ed. 2020
edited by Pavel Kurasov, Ari Laptev, Sergey Naboko, Barry Simon
出版情報: Cham : Springer International Publishing : Imprint: Birkhäuser, 2020
シリーズ名: Operator Theory: Advances and Applications ; 276
オンライン: https://doi.org/10.1007/978-3-030-31531-3
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目次情報: 続きを見る
Part I - Memorial Contributions
Life and career
Water-colours by Boris Pavlov
Family and leisure
Pavlov's mathematics
Part II - Research Papers
Singular perturbations of unbounded selfadjoint operators. Reverse approach
Generic asymptotics of resonance counting function for Schrödinger point interactions
Spectral clusters, asymmetric spaces, and boundary control for Schrodinger equation with strong singularities
The second Weyl coefficient for a first order system
A Lieb-Thirring type inequality for magnetic Schrödinger operators with a radial symmetry
Scattering matrices and Weyl functions of quasi boundary triples
On the spectrum of the quantum Rabi model
Scattering theory for a class of non-selfadjoint extensions of symmetric operators
Asymptotics of Chebyshev polynomials, III. Sets saturating Szego, Schiefermayr, and Totitk-Widom bounds
Solvability and complex limit characteristics
Quantization of Gaussians
A resonance interaction of seismogravitational modes of tectonic plates
On positivity preserving, translation invariant, operators in Lp(Rn)m
The distribution of path lengths on directed weighted graphs
Diagonalization of indenite saddle point forms
Solutions of Gross-Pitaevskii equation with periodic potential in dimension two
The Integral Transform of N.I. Akhiezer
On Gaussian random matrices coupled to the discrete Laplacian
Modern results in the spectral analysis for a class of integral-difference operators and application to physical processes
Inverse problem for integral-difference operators on graphs
Quantum graph in a magnetic field and resonance states completeness
On Zd-symmetry of spectra of some nuclear operators
Spectral monotonicity for Schrödinger operators on metric graphs
Linear Operators and Operator Functions Associated with Spectral Boundary Value Problem
Part I - Memorial Contributions
Life and career
Water-colours by Boris Pavlov
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9. Spectral and Scattering Theory for Ordinary Differential Equations : Vol. I: Sturm–Liouville Equations. 1st ed. 2020
by Christer Bennewitz, Malcolm Brown, Rudi Weikard
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: Universitext ;
オンライン: https://doi.org/10.1007/978-3-030-59088-8
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目次情報: 続きを見る
1 Introduction
2 Hilbert space
3 Abstract spectral theory
4 Sturm–Liouville equations
5 Left-definite Sturm–Liouville equations
6 Oscillation, spectral asymptotics and special functions
7 Uniqueness of the inverse problem
8 Scattering
A Functional analysis
B Stieltjes integrals
C Schwartz distributions
D Ordinary differential equations
E Analytic functions
F The Camassa–Holm equation
References
Symbol Index
Subject Index
1 Introduction
2 Hilbert space
3 Abstract spectral theory
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10. An Invitation to Unbounded Representations of ∗-Algebras on Hilbert Space. 1st ed. 2020
by Konrad Schmüdgen
出版情報: Cham : Springer International Publishing : Imprint: Springer, 2020
シリーズ名: Graduate Texts in Mathematics ; 285
オンライン: https://doi.org/10.1007/978-3-030-46366-3
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目次情報: 続きを見る
General Notation
1 Prologue: The Algebraic Approach to Quantum Theories
2 ∗-Algebras
3 O*-Algebras
4 ∗-Representations
5 Positive Linear Functionals
6 Representations of Tensor Algebras
7 Integrable Representations of Commutative ∗-Algebras
8 The Weyl Algebra and the Canonical Commutation Relation
9 Integrable Representations of Enveloping Algebras
10 Archimedean Quadratic Modules and Positivstellensätze
11 The Operator Relation XX*=F(X*X)
12 Induced ∗-Representations
13 Well-behaved ∗-Representations
14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space
B C*-Algebras and Representations
C Locally Convex Spaces and Separation of Convex Sets
References
Symbol Index
Subject Index
General Notation
1 Prologue: The Algebraic Approach to Quantum Theories
2 ∗-Algebras