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By Hans G. Feichtinger, Thomas Strohmer

ISBN-10: 1461201330

ISBN-13: 9781461201335

ISBN-10: 1461266270

ISBN-13: 9781461266273

The utilized and Numerical Harmonic research (ANHA) e-book sequence goals to supply the engineering, mathematical, and clinical groups with major advancements in harmonic research, starting from summary har­ monic research to simple purposes. The identify of the sequence displays the im­ portance of purposes and numerical implementation, yet richness and relevance of functions and implementation count essentially at the constitution and intensity of theoretical underpinnings. hence, from our perspective, the interleaving of thought and purposes and their inventive symbi­ otic evolution is axiomatic. Harmonic research is a wellspring of rules and applicability that has flour­ ished, built, and deepened through the years inside of many disciplines and via inventive cross-fertilization with different components. The elaborate and primary dating among harmonic research and fields similar to sig­ nal processing, partial differential equations (PDEs), and photo processing is mirrored in our cutting-edge ANHA sequence. Our imaginative and prescient of contemporary harmonic research contains mathematical components comparable to wavelet concept, Banach algebras, classical Fourier research, time­ frequency research, and fractal geometry, in addition to the varied issues that impinge on them.

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London Math. Soc. 63 (2001),205-214. [20] G. H. Hardy, A theorem concerning Fourier transforms, J. London Math. Soc. 8 (1933),227-231. [21] V. Havin and B. Joricke, The uncertainty principle in harmonic analysis, Springer-Verlag, Berlin, 1994. 30 Kaxlheinz Gr6chenig [22] F. Hlawatsch and G. F. Boudreaux-Bartels, Linear and quadratic time-frequency signal representations, IEEE Signal Proc. Magazine 9 (1992), no. 2, 21 - 67. [23] J. A. Hogan and J. D. Lakey, Embeddings and uncertainty principles for generalized modulation spaces, Modern Sampling Theory Mathematics and Applications (J.

17] K. Grochenig, An uncertainty principle related to the Poisson summation formula, Studia Math. 121 (1996), no. 1,87-104. [18] K. Grochenig, Foundations of time-frequency analysis, Birkhiiuser, Boston, 2001. [19] K. Grochenig and G. Zimmermann, Hardy's theorem and the shorttime Fourier transform of Schwartz functions, J. London Math. Soc. 63 (2001),205-214. [20] G. H. Hardy, A theorem concerning Fourier transforms, J. London Math. Soc. 8 (1933),227-231. [21] V. Havin and B. Joricke, The uncertainty principle in harmonic analysis, Springer-Verlag, Berlin, 1994.

3 the L1-version is not applicable to all functions f, 9 E L2 (lRd ). The subspace of f, 9 E L2 (lRd) such that Vg fELl (JR2d) is the so-called Feichtinger algebra and is an important function class in harmonic analysis and time-frequency analysis [11, 12, 18]. 4 we have seen that the measure of the support of f 181 j, W(f, g), A(f, g) and Vgf is either 0 or 00. In other words, the support of a time-frequency representation is not a good measure for the time-frequency 2. Uncertainty Principles for Time-Frequency Representations 23 concentration, and uncertainty principles involving the strict support are only of a qualitative nature.

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Advances in Gabor Analysis by Hans G. Feichtinger, Thomas Strohmer

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