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OverviewThis book is an outgrowth of courses given by me for graduate students at York University in the past ten years. The actual writing of the book in this form was carried out at York University, Peking University, the Academia Sinica in Beijing, the University of California at Irvine, Osaka University, and the University of Delaware. The idea of writing this book was ?rst conceived in the summer of 1989, and the protracted period of gestation was due to my daily duties as a professor at York University. I would like to thank Professor K. C. Chang, of Peking University; Professor Shujie Li, of the Academia Sinica in Beijing; Professor Martin Schechter, of the University of California at Irvine; Professor Michihiro Nagase, of Osaka University; and Professor M. Z. Nashed, of the University of Delaware, for providing me with stimulating environments for the exchange of ideas and the actual writing of the book. We study in this book the properties of pseudo-differential operators arising in quantum mechanics, ?rst envisaged in [33] by Hermann Weyl, as bounded linear 2 n operators on L (R ). Thus, it is natural to call the operators treated in this book Weyl transforms. Full Product DetailsAuthor: M.W. WongPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1998 Dimensions: Width: 15.50cm , Height: 0.90cm , Length: 23.50cm Weight: 0.272kg ISBN: 9781475771749ISBN 10: 1475771746 Pages: 160 Publication Date: 08 March 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsPrerequisite Topics in Fourier Analysis.- The Fourier-Wigner Transform.- The Wigner Transform.- The Weyl Transform.- Hilbert-Schmidt Operators on L2(?n).- The Tensor Product in L2(?n).- H*-Algebras and the Weyl Calculus.- The Heisenberg Group.- The Twisted Convolution.- The Riesz-Thorin Theorem.- Weyl Transforms with Symbols in Lr(?2n), 1 ? r ? 2.- Weyl Transforms with Symbols in L?(?2n).- Weyl Transforms with Symbols in Lr(?2n), 2 r < ?.- Compact Weyl Transforms.- Localization Operators.- A Fourier Transform.- Compact Localization Operators.- Hermite Polynomials.- Hermite Functions.- Laguerre Polynomials.- Hermite Functions on ?.- Vector Fields on ?.- Laguerre Formulas for Hermite Functions on ?.- Weyl Transforms on L2(?) with Radial Symbols.- Another Fourier Transform.- A Class of Compact Weyl Transforms on L2(?).- A Class of Bounded Weyl Transforms on L2(?).- A Weyl Transform with Symbol in S’(?2).- The Symplectic Group.- Symplectic Invariance of Weyl Transforms.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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