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Symplectic Methods in Harmonic Analysis and in Mathematical Physics

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Cover of 'Symplectic Methods in Harmonic Analysis and in Mathematical Physics'

Table of Contents

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    Book Overview
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    Chapter 1 Hamiltonian Mechanics in a Nutshell
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    Chapter 2 The Symplectic Group
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    Chapter 3 Free Symplectic Matrices
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    Chapter 4 The Group of Hamiltonian Symplectomorphisms
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    Chapter 5 Symplectic Capacities
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    Chapter 6 Uncertainty Principles
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    Chapter 7 The Metaplectic Group
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    Chapter 8 Heisenberg–Weyl and Grossmann–Royer Operators
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    Chapter 9 Cross-ambiguity and Wigner Functions
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    Chapter 10 The Weyl Correspondence
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    Chapter 11 Coherent States and Anti-Wick Quantization
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    Chapter 12 Hilbert–Schmidt and Trace Class Operators
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    Chapter 13 Density Operator and Quantum States
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    Chapter 14 Shubin’s Global Operator Calculus
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    Chapter 15 The Schrödinger Equation
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    Chapter 16 The Feichtinger Algebra
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    Chapter 17 The Modulation Spaces $$M_s^q$$
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    Chapter 18 Bopp Pseudo-differential Operators
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    Chapter 19 Applications of Bopp Quantization
Attention for Chapter 5: Symplectic Capacities
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