close
1.

図書
図書
1. Mathematical scattering theory
Hellmut Baumgärtel, Manfred Wollenberg
出版情報: Basel [Switzerland] : Birkhäuser, 1983  449 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; OT 9
所蔵情報: loading…
2.

図書
図書
2. Operator methods in quantum mechanics
Martin Schechter
出版情報: New York : North Holland, c1981  xx, 324 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Acknowledgments
A Message to the Reader
List of Symbols
One-Dimensional Motion / Chapter 1.：
Position / 1.1.：
Mathematical Expectation / 1.2.：
Momentum / 1.3.：
Energy / 1.4.：
Observables / 1.5.：
Operators / 1.6.：
Functions of Observables / 1.7.：
Self-Adjoint Operators / 1.8.：
Hilbert Space / 1.9.：
The Spectral Theorem / 1.10.：
Exercises
The Spectrum / Chapter 2.：
The Resolvent / 2.1.：
Finding the Spectrum / 2.2.：
The Position Operator / 2.3.：
The Momentum Operator / 2.4.：
The Energy Operator / 2.5.：
The Potential / 2.6.：
A Class of Functions / 2.7.：
The Spectrum of H / 2.8.：
The Essential Spectrum / Chapter 3.：
An Example / 3.1.：
A Calculation / 3.2.：
Finding the Eigenvalues / 3.3.：
The Domain of H / 3.4.：
Back to Hilbert Space / 3.5.：
Compact Operators / 3.6.：
Relative Compactness / 3.7.：
Proof of Theorem 3.7.5 / 3.8.：
The Negative Eigenvalues / Chapter 4.：
The Possibilities / 4.1.：
Forms Extensions / 4.2.：
The Remaining Proofs / 4.3.：
Negative Eigenvalues / 4.4.：
Existence of Bound States / 4.5.：
Existence of Infinitely Many Bound States / 4.6.：
Existence of Only a Finite Number of Bound States / 4.7.：
Another Criterion / 4.8.：
Estimating the Spectrum / Chapter 5.：
Introduction / 5.1.：
Some Crucial Lemmas / 5.2.：
A Lower Bound for the Spectrum / 5.3.：
Lower Bounds for the Essential Spectrum / 5.4.：
An Inequality / 5.5.：
Bilinear Forms / 5.6.：
Intervals Containing the Essential Spectrum / 5.7.：
Coincidence of the Essential Spectrum with an Interval / 5.8.：
The Harmonic Oscillator / 5.9.：
The Morse Potential / 5.10.：
Scattering Theory / Chapter 6.：
Time Dependence / 6.1.：
Scattering States / 6.2.：
Properties of the Wave Operators / 6.3.：
The Domains of the Wave Operators / 6.4.：
Local Singularities / 6.5.：
Long-Range Potentials / Chapter 7.：
The Coulomb Potential / 7.1.：
Some Examples / 7.2.：
The Estimates / 7.3.：
The Derivatives of V(x) / 7.4.：
The Relationship Between X[subscript t] and V(x) / 7.5.：
An Identity / 7.6.：
The Reduction / 7.7.：
Mollifiers / 7.8.：
Time-Independent Theory / Chapter 8.：
The Resolvent Method / 8.1.：
The Theory / 8.2.：
A Simple Criterion / 8.3.：
The Application / 8.4.：
Completeness / Chapter 9.：
Definition / 9.1.：
The Abstract Theory / 9.2.：
Some Identities / 9.3.：
Another Form / 9.4.：
The Unperturbed Resolvent Operator / 9.5.：
The Perturbed Operator / 9.6.：
Analytic Dependence / 9.7.：
Projections / 9.9.：
An Analytic Function Theorem / 9.10.：
The Combined Results / 9.11.：
Absolute Continuity / 9.12.：
The Intertwining Relations / 9.13.：
Strong Completeness / 9.14.：
The More Difficult Problem / 10.1.：
The Technique / 10.2.：
Verification for the Hamiltonian / 10.4.：
An Extension / 10.5.：
The Principle of Limiting Absorption / 10.6.：
Oscillating Potentials / Chapter 11.：
A Surprise / 11.1.：
The Hamiltonian / 11.2.：
A Variation / 11.3.：
Examples / 11.5.：
Eigenfunction Expansions / Chapter 12.：
The Usefulness / 12.1.：
The Problem / 12.2.：
Operators on L[superscript p] / 12.3.：
Weighted L[superscript p]-Spaces / 12.4.：
Extended Resolvents / 12.5.：
The Formulas / 12.6.：
Some Consequences / 12.7.：
Summary / 12.8.：
Restricted Particles / Chapter 13.：
A Particle Between Walls / 13.1.：
The Energy Levels / 13.2.：
Compact Resolvents / 13.3.：
One Opaque Wall / 13.4.：
Scattering on a Half-Line / 13.5.：
The Spectral Resolution for the Free Particle on a Half-Line / 13.6.：
Hard-Core Potentials / Chapter 14.：
Local Absorption / 14.1.：
The Modified Hamiltonian / 14.2.：
The Resolvent Operator for H[subscript 1] / 14.3.：
The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0]) / 14.4.：
Propagation / 14.5.：
Proof of Theorem 14.5.1 / 14.6.：
Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0]) / 14.7.：
The Wave Operators W[subscript plus or minus] (H, H[subscript 1]) / 14.8.：
A Regularity Theorem / 14.9.：
A Family of Spaces / 14.10.：
The Invariance Principle / Chapter 15.：
A Simple Result / 15.1.：
Trace Class Operators / 15.3.：
The Abstract Theorem / 16.1.：
Hilbert--Schmidt Operators / 16.2.：
The Fourier Transform / 16.4.：
Exercises A
Exercises B / Appendix B.：
Holder's Inequality and Banach Space / Appendix C.：
Bibliography
Index
Preface
Acknowledgments
A Message to the Reader
3.

図書
図書
3. Interpolation of operators
Colin Bennett, Robert Sharpley
出版情報: Boston ; Tokyo : Academic Press, c1988  xiv, 469 p. ; 24 cm
シリーズ名: Pure and applied mathematics ; v. 129
所蔵情報: loading…
目次情報: 続きを見る
Banach Function Spaces
Rearrangement-Invariant Banach Function Spaces
Interpolation of Operators on Rearrangement-Invariant Spaces
The Classical Interpolation Theorems
The K-Method
Each chapter includes references
Index
Banach Function Spaces
Rearrangement-Invariant Banach Function Spaces
Interpolation of Operators on Rearrangement-Invariant Spaces
4.

図書
図書
4. Topics in operator theory and interpolation : essays dedicated to M.S. Livsic on the occasion of his 70th birthday (: Basel ; : Boston)
edited by I. Gohberg
出版情報: Basel ; Boston : Birkhäuser Verlag, 1988  243 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 29
所蔵情報: loading…
5.

図書
図書
5. Basic operator theory
Israel Gohberg, Seymour Goldberg ; edited by I. Gohberg
出版情報: Boston ; Basel : Birkhäuser, 1981  xiii, 285 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Introduction
Hilbert Spaces / I：
Bounded Linear Operators on Hilbert Spaces / II：
Spectral Theory of Compact Self Adjoint Operators / III：
Spectral Theory of Integral Operators / IV：
Oscillations of an Elastic String / V：
Operational Calculus with Applications / VI：
Solving Linear Equations by Iterative Methods / VII：
Further Developments of the Spectral Theorem / VIII：
Banach Spaces / IX：
Linear Operators on a Banach Space / X：
Compact Operators on a Banach Space / XI：
Non-Linear Operators / XII：
Appendix 1. Countable Sets and Separable Hilbert Spaces
Appendix 2. Lebesgue Integration and LP Spaces
Appendix 3. Proof of the Hahn-Banach Theorem
Appendix 4. Proof of the Closed Graph Theorem
Suggested Reading
References
Index
Introduction
Hilbert Spaces / I：
Bounded Linear Operators on Hilbert Spaces / II：
6.

図書
図書
6. Topics in operator theory : Constantin Apostol memorial issue (: Boston ; : Basel)
edited by I. Gohberg
出版情報: Basel ; Boston : Birkhäuser Verlag, 1988  vii, 274 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 32
所蔵情報: loading…
7.

図書
図書
7. Sturm-Liouville operators and applications (: U.S.)
Vladimir A. Marchenko ; translated from the Russian by A. Iacob
出版情報: Basel : Birkhäuser Verlag, 1986  xi, 367 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; v. 22
所蔵情報: loading…
8.

図書
図書
8. Eigenvalues and s-numbers
Albrecht Pietsch
出版情報: Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987  360 p. ; 24 cm
シリーズ名: Cambridge studies in advanced mathematics ; 13
所蔵情報: loading…
9.

図書
図書
9. Introduction to operator theory and invariant subspaces
Bernard Beauzamy
出版情報: Amsterdam ; Tokyo : North-Holland , New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988  xiv, 358 p. ; 23 cm
シリーズ名: North-Holland mathematical library ; v. 42
所蔵情報: loading…
10.

図書
図書
10. Applications of functional analysis and operator theory
V. Hutson and J. S. Pym
出版情報: London : Academic Press, 1980  xi, 389 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 146
所蔵情報: loading…
目次情報: 続きを見る
Preface
Acknowledgements
Banach Spaces / 1：
Introduction / 1.1：
Vector Spaces / 1.2：
Normed Vector Spaces / 1.3：
Hilbert Space Problems / 1.4：
Lebesgue Integration and the Lp Spaces / 2：
The Measure of a Set / 2.1：
Measurable Functions / 2.3：
Integration / 2.4：
The Lp Spaces / 2.5：
Applications Problems / 2.6：
Foundations of Linear Operator Theory / 3：
The Basic Terminology of Operator Theory / 3.1：
Some Algebraic Properties of Linear Operators / 3.3：
Continuity and Boundedness / 3.4：
Some Fundamental Properties of Bounded Operators / 3.5：
First Results on the Solution of the Equation Lf=g / 3.6：
Introduction to Spectral Theory / 3.7：
Closed Operators and Differential Equations Problems / 3.8：
Introduction to Nonlinear Operators / 4：
Preliminaries / 4.1：
The Contraction Mapping Principle / 4.3：
The Frechet Derivative / 4.4：
Newton's Method for Nonlinear Operators Problems / 4.5：
Compact Sets in Banach Spaces / 5：
Definitions / 5.1：
Some Consequences of Compactness / 5.3：
Some Important Compact Sets of Functions Problems / 5.4：
The Adjoint Operator / 6：
The Dual of a Banach Space / 6.1：
Weak Convergence / 6.3：
Hilbert Space / 6.4：
The Adjoint of a Bounded Linear Operator / 6.5：
Bounded Self-adjoint Operators -- Spectral Theory / 6.6：
The Adjoint of an Unbounded Linear Operator in Hilbert Space Problems / 6.7：
Linear Compact Operators / 7：
Examples of Compact Operators / 7.1：
The Fredholm Alternative / 7.3：
The Spectrum / 7.4：
Compact Self-adjoint Operators / 7.5：
The Numerical Solution of Linear Integral Equations Problems / 7.6：
Nonlinear Compact Operators and Monotonicity / 8：
The Schauder Fixed Point Theorem / 8.1：
Positive and Monotone Operators in Partially Ordered Banach Spaces Problems / 8.3：
The Spectral Theorem / 9：
Background to the Spectral Theorem / 9.1：
The Spectral Theorem for Bounded Self-adjoint Operators / 9.4：
The Spectrum and the Resolvent / 9.5：
Unbounded Self-adjoint Operators / 9.6：
The Solution of an Evolution Equation Problems / 9.7：
Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations / 10：
Extensions of Symmetric Operators / 10.1：
Formal Ordinary Differential Operators: Preliminaries / 10.3：
Symmetric Operators Associated with Formal Ordinary Differential Operators / 10.4：
The Construction of Self-adjoint Extensions / 10.5：
Generalized Eigenfunction Expansions Problems / 10.6：
Linear Elliptic Partial Differential Equations / 11：
Notation / 11.1：
Weak Derivatives and Sobolev Spaces / 11.3：
The Generalized Dirichlet Problem / 11.4：
Fredholm Alternative for Generalized Dirichlet Problem / 11.5：
Smoothness of Weak Solutions / 11.6：
Further Developments Problems / 11.7：
The Finite Element Method / 12：
The Ritz Method / 12.1：
The Rate of Convergence of the Finite Element Method Problems / 12.3：
Introduction to Degree Theory / 13：
The Degree in Finite Dimensions / 13.1：
The Leray-Schauder Degree / 13.3：
A Problem in Radiative Transfer Problems / 13.4：
Bifurcation Theory / 14：
Local Bifurcation Theory / 14.1：
Global Eigenfunction Theory Problems / 14.3：
References
List of Symbols
Index
Preface
Acknowledgements
Banach Spaces / 1：
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼