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Titlebook: Coherent States, Wavelets and Their Generalizations; Syed Twareque Ali,Jean-Pierre Antoine,Jean-Pierre Textbook 20001st edition Springer

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Square Integrable and Holomorphic Kernels,iterature. While the very general reproducing kernel Hilbert spaces, constructed in the last chapter, were spaces of vector-valued functions, they were not assumed to be Hilbert spaces of square integrable functions, with respect to any measure. Most reproducing kernel Hilbert spaces that arise in p
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CS of General Semidirect Product Groups,of irreducible subrepresentations, all square integrable. These groups were of the general form . ℝ. ⋊ ., where . was an .-dimensional subgroup of .(.ℝ) and its action on the dual space gave rise to open free orbits. In this chapter, we generalize this setting and consider semidirect products of the
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Wavelets,in the last few years. The genesis of the method is interesting for the present book, so we will spend a paragraph outlining it. After the empirical discovery by Jean Morlet (who was analyzing microseismic data in the context of oil exploration [152]), it was recognized from the very beginning by Gr
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Discrete Wavelet Transforms,al processing, a tight frame is almost as good as an orthonormal basis. Actually, if one stays with the standard wavelets, as we have done so far, one cannot do better, since these wavelets do not generate any orthonormal basis (like the usual coherent states). There are cases, however, in which an
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Wavelets Related to Other Groups,er instances (then spheres of dimension higher than two might occur). If one is interested only in very local features, one may ignore the curvature and work on the tangent plane, but when global aspects become important (description of plate tectonics on the Earth, for instance), one needs a genuin
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