Titlebook: Coherent States, Wavelets, and Their Generalizations; Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Book 2014Latest edition Springer

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Square Integrable and Holomorphic Kernels,n-angle variables, which are then used to extend the theory to a non-holomorphic set-up, namely, the so-called Gazeau–Klauder CS. The latter in turn lead to probabilistic considerations, that will be the focus of Chap. 11.

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Coherent States from Square Integrable Representations,. Several concrete examples are presented. Finally we generalize the theory to representations that are only square integrable on a homogeneous space. This allows one to treat CS of the Gilmore-Perelomov type and, in particular, CS of the Galilei group.

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Wavelets on Manifolds,g to . ordinary dilations on a tangent plane by an inverse stereographic projection. Next we describe briefly a number of techniques for obtaining discrete wavelets on .. Then we extend the analysis to wavelets on other manifolds, such as conic sections, a torus, general surfaces of revolution or graphs.

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The Discretization Problem: Frames, Sampling, and All That,ames associated with affine semidirect product groups, such as the affine Weyl–Heisenberg group or the affine Poincaré group. Finally we turn to groups without dilations, in particular, the Poincaré groups in 1+1 and 1+3 dimensions.

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Book 2014Latest editionherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory

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Discrete Wavelet Transforms,lets, by which we mean wavelets based on different numbers, replacing, for instance, the dilation factor 2 by the golden mean . (we speak then of .-wavelets) or arbitrary real numbers, which lead to Pisot wavelets.

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