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The Wigner Transform

Maurice de Gosson
Publisher: 
World Scientific
Publication Date: 
2018
Number of Pages: 
229
Format: 
Paperback
Series: 
Advanced Textbooks in Mathematics
Price: 
58.00
ISBN: 
9781786343093
Category: 
Monograph
We do not plan to review this book.
  • General Mathematical Framework:
    • Phase Space Translations and Reflections
    • The Cross-Wigner Transform
    • The Cross-Ambiguity Function
    • Weyl Operators
    • Symplectic Covariance
    • The Moyal Identity
    • The Feichtinger Algebra
    • The Cohen Class
    • Gaussians and Hermite Functions
    • Sub-Gaussian Estimates
  • Applications to Quantum Mechanics:
    • Moyal Star Product and Twisted Convolution
    • Probabilistic Interpretation of the Wigner Transform
    • Mixed Quantum States and the Density Operator
    • The KLM Conditions and the Narcowich–Wigner Spectrum
    • Wigner Transform and Quantum Blobs
  • Appendices:
    • A: Sp(n) and Mp(n)
    • B: The Symplectic Fourier Transform
    • C: Symplectic Diagonalization
    • D: Symplectic Capacities