The sticky technical issues of real analysis disappear entirely, thus allowing us to focus on the big picture.We shall begin by considering cyclic groups, for the unit circle, on which the theory of Fourier series is developed, can be approximated by regular N -gons as ...
Fourier analysis Trigonometric interpolation Posted on 5 November 2024 by John Suppose you want to interpolate a set of data points with a combination of sines and cosines. One way to approach this problem would be to set up a system of equations for the coefficients of the sines and cosines...
PDF (2458 K) | View Record in Scopus | Citing articles (14) 2. M. Eguchi, Some properties of Fourier transform on Riemannian symmetric spaces, in“Proceedings of the France-Japan Symposium on Harmonic Analysis on Lie Groups,” Lecture Notes on Mathematics, Springer-Verlag, Berlin/New York...
H. Young in 1912 to generalize Parseval's theoremfor Fourier series to other LP-classes, and they extendnaturally in the context of analysis on locally compactabelian groups. For the circle group T;R/Z thecorresponding inequalities are sharp, but for the Fouriertransform on LP(R), K. I. ...
Fourier Analysis on Groups The Fourier transform in classical mathematical analysis is defined in terms of exponential functions exp ( jwx ) that may be thought of as the characters ... W Rudin,L Bers,R Courant,... - 《Physics Today》 被引量: 3363发表: 1962年 Fourier Integrals. (Scientifi...
View PDFView articleView in ScopusGoogle Scholar [DR] P. Diaconis and D. Rockmore, Efficient computation of Fourier transforms on finite groups, to appear. Google Scholar [DS] P Diaconis, M Shashahani Products of random matrices as they arise in the study of random walks on groups Contemporar...
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possibly vector-valued. Still further generalization is possible to functions on groups, which, besides the original Fourier transform on R or Rn (viewed as groups under addition), notably includes the discrete-time Fourier transform (DTFT, group = Z), the discrete Fourier transform (DFT, group...
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Modulation Spaces on Locally Compact Abelian Groups; Universität Wien, Mathematisches Institut: Vienna, Austria, 1983. [Google Scholar] Gröchenig, K.; Heil, C. Modulation Spaces and Pseudodifferential Operators. Integr. Equ. Oper. Theory 1999, 34, 439–457. [Google Scholar] [CrossRef] ...