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Download Symplectic geometry and Fourier analysis (Lie groups ; v. 5) djvu

Download Symplectic geometry and Fourier analysis (Lie groups ; v. 5) djvu

by Nolan R Wallach

Author: Nolan R Wallach
Subcategory: Mathematics
Language: English
Publisher: Math Sci Press (1977)
Pages: 436 pages
Category: Math and Science
Rating: 4.1
Other formats: mbr doc azw rtf

It touches on, among other things, the quantization program of Konstant, Souriau and others The book by Simms and Woodhouse is comparable to this one, in that regard. The introductory chapter on differential geometry is a handy resource of basic material needed in the sequel. The appendix by R. Hermann on quantum mechanics is enlightening (as his writings always were, in my mind).

This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors. The monograph is geared toward readers who have taken a basic course in differential manifolds and elementary functional analysis. The first chapters cover certain geometric preliminaries, advancing to discussions of symplectic geometry and the application of its concepts to the action of a Lie group on a symplectic manifold

In this book, a new Fourier analysis approach is discussed. The idea is to express certain geometric properties of bodies in terms of Fourier analysis and to use harmonic analysis methods to solve geometric problems.

In this book, a new Fourier analysis approach is discussed.

The symplectic geometry of closed equilateral random walks in 3-space Cantarella, Jason and Shonkwiler . Geometry of pseudodifferential algebra bundles and Fourier integral operators Mathai, Varghese and Melrose, Richard . Duke Mathematical Journal, 2017.

The symplectic geometry of closed equilateral random walks in 3-space Cantarella, Jason and Shonkwiler, Clayton, The Annals of Applied Probability, 2016. Spin-quantization commutes with reduction Paradan, Paul-Emile, Journal of Symplectic Geometry, 2012. A convexity theorem for torus actions on contact manifolds Lerman, Eugene, Illinois Journal of Mathematics, 2002.

Suitable for graduate students in mathematics, this monograph covers differential and symplectic geometry, homogeneous symplectic manifolds, Fourier analysis, metaplectic representation, quantization, Kirillov theory. This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors

This book derives from author Nolan R. The first chapters cover certain geometric preliminaries, advancing to discussions of symplectic geometry and the application of its concepts to the action of a Lie group on a symplectic manifold

Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some . N. R. Wallach, Symplectic geometry and Fourier analysis, Math. Sci. Press, Brookline, Mass.

Symplectic geometry is a branch of differential geometry studying symplectic manifolds and some generalizations; it originated as a formalization of the mathematical apparatus of classical mechanics and geometric optics (and the related WKB-method in quantum mechanics and, more generally, the method of stationary phase in harmonic analysis). A wider branch including symplectic geometry is Poisson geometry and a sister branch in odd dimensions is contact geometry.

oceedings{Gallier2011NotesOD, title {Notes on Differential Geometry and Lie Groups}, author {Jean H. Gallier and Jocelyn Quaintance}, year {2011} }. Jean H. Gallier, Jocelyn Quaintance. However, for any point p on the manifold M and for any chart whose domain contains p, there is a convenient basis of the tangent space Tp(M). The third definition is also the most convenient one to define vector fields.

Classical Fourier analysis has an exact counterpart in group theory and in some . The symplectic homogeneous space (Of, ωf ) leads to a. unitary representation class ∈ N, as follows.

Classical Fourier analysis has an exact counterpart in group theory and in some areas of geometry. Here I’ll describe how this goes for nilpotent Lie groups, for a class of Riemannian manifolds closely related to a nilpotent Lie group structure. There are also some innite dimensional analogs but I won’t go into that here. As indicated earlier, Fourier analysis for nilpotent Lie groups N and commutative nil-manifolds (N ⋊ K)/K, where N has square integrable representations, has recently been extended to some classes direct limit groups and spaces.

There are several books on symplectic geometry, but I still took the trouble of writing up lecture notes. The reason is that this one semester course was aiming for students at the beginning of their masters.

Former library book, paperback, 436 pages, 1977 edition