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1.

電子ブック
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1. Homogenization of Partial Differential Equations
by Vladimir A. Marchenko, Evgueni Ya. Khruslov ; edited by Anne Boutet de Monvel, Gerald Kaiser, C. Berenstein, M. Berry, P. Blanchard, M. Eastwood, A. S. Fokas, D. Sternheimer, C. Tracy
出版情報: Boston, MA : Birkhäuser Boston, 2006
シリーズ名: Progress in Mathematical Physics ; 46
オンライン: http://dx.doi.org/10.1007/978-0-8176-4468-0
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2.

電子ブック
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2. Functions, Spaces, and Expansions : Mathematical Tools in Physics and Engineering
by Ole Christensen
出版情報: Boston : Springer Science+Business Media, LLC, 2010
シリーズ名: Applied and Numerical Harmonic Analysis ;
オンライン: http://dx.doi.org/10.1007/978-0-8176-4980-7
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3.

電子ブック
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3. Quantum Field Theory III: Gauge Theory : A Bridge between Mathematicians and Physicists
by Eberhard Zeidler
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2011
オンライン: http://dx.doi.org/10.1007/978-3-642-22421-8
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4.

電子ブック
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4. Hypernumbers and Extrafunctions : Extending the Classical Calculus
by Mark Burgin
出版情報: New York, NY : Springer New York, 2012
シリーズ名: SpringerBriefs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-1-4419-9875-0
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5.

電子ブック
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5. Partial Differential Equations 2 : Functional Analytic Methods. 2nd ed. 2012
by Friedrich Sauvigny
出版情報: London : Springer London, 2012
シリーズ名: Universitext ;
オンライン: http://dx.doi.org/10.1007/978-1-4471-2984-4
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電子ブック
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6. Recent Advances in Matrix and Operator Theory
edited by Joseph A. Ball, Yuli Eidelman, J. William Helton, Vadim Olshevsky, James Rovnyak
出版情報: Basel : Birkhäuser Verlag AG, 2008
シリーズ名: Operator Theory: Advances and Applications ; 179
オンライン: http://dx.doi.org/10.1007/978-3-7643-8539-2
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7.

電子ブック
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7. Quantum Field Theory II: Quantum Electrodynamics : A Bridge between Mathematicians and Physicists
by Eberhard Zeidler
出版情報: Berlin, Heidelberg : Springer-Verlag Berlin Heidelberg, 2009
オンライン: http://dx.doi.org/10.1007/978-3-540-85377-0
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8.

電子ブック
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8. 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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電子ブック
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9. Quantum Theory for Mathematicians
by Brian C. Hall
出版情報: New York, NY : Springer New York : Imprint: Springer, 2013
シリーズ名: Graduate Texts in Mathematics ; 267
オンライン: http://dx.doi.org/10.1007/978-1-4614-7116-5
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目次情報: 続きを見る
1 The Experimental Origins of Quantum Mechanics
2 A First Approach to Classical Mechanics
3 A First Approach to Quantum Mechanics
4 The Free Schrödinger Equation
5 A Particle in a Square Well
6 Perspectives on the Spectral Theorem
7 The Spectral Theorem for Bounded Self-Adjoint Operators: Statements
8 The Spectral Theorem for Bounded Sef-Adjoint Operators: Proofs
9 Unbounded Self-Adjoint Operators
10 The Spectral Theorem for Unbounded Self-Adjoint Operators
11 The Harmonic Oscillator
12 The Uncertainty Principle
13 Quantization Schemes for Euclidean Space
14 The Stone–von Neumann Theorem
15 The WKB Approximation
16 Lie Groups, Lie Algebras, and Representations
17 Angular Momentum and Spin
18 Radial Potentials and the Hydrogen Atom
19 Systems and Subsystems, Multiple Particles
V Advanced Topics in Classical and Quantum Mechanics
20 The Path-Integral Formulation of Quantum Mechanics
21 Hamiltonian Mechanics on Manifolds
22 Geometric Quantization on Euclidean Space
23 Geometric Quantization on Manifolds
A Review of Basic Material
References. - Index
1 The Experimental Origins of Quantum Mechanics
2 A First Approach to Classical Mechanics
3 A First Approach to Quantum Mechanics
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10. Positive Linear Maps of Operator Algebras
by Erling Størmer
出版情報: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013
シリーズ名: Springer Monographs in Mathematics ;
オンライン: http://dx.doi.org/10.1007/978-3-642-34369-8
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目次情報: 続きを見る
Introduction
1 Generalities for positive maps
2 Jordan algebras and projection maps
3 Extremal positive maps
4 Choi matrices and dual functionals
5 Mapping cones
6 Dual cones
7 States and positive maps
8 Norms of positive maps
Appendix: A.1 Topologies on B(H)
A.2 Tensor products
A.3 An extension theorem
Bibliography
Index
Introduction
1 Generalities for positive maps
2 Jordan algebras and projection maps