منابع مشابه
Generalized Paley-Wiener Theorems
Non-harmonic Fourier transform is useful for the analysis of transient signals, where the integral kernel is from the boundary value of Möbius transform. In this note, we study the Paley–Wiener type extension theorems for the non-harmonic Fourier transform. Two extension theorems are established by using real variable techniques.
متن کاملPaley-wiener-type Theorems
The Fourier transforms of functions with compact and convex supports in R are described. The Fourier transforms of functions with nonconvex and unbounded supports are also considered.
متن کاملTrace Paley - Wiener Theorem
w Statement of the theorem 1.1. Let G be a reductive p-adic group. A smooth representation (~', E) of the group G on a complex vector space E is called a G-module. Usually we shorten the notation and write w or E. Let d~(G) be the category of G-modules, Irr G the set of equivalence classes of irreducible G-modules, and R (G) the Grothendieck group of G-modules of fnite length; R(G) is a free ab...
متن کاملThe Trace Paley Wiener Theorem for Schwartz Functions
on 11temp (G(F)) . The object of this note is to characterize the image of the map. Results of this nature are well known. The case of the Hecke algebra on G(F), which is in fact more difficult, was established in [3] and [5]. A variant of the problem for the smooth functions of compact support on a real group was solved in [4]. For the Schwartz space, one has a choice of several possible appro...
متن کاملPaley–wiener Theorems for the Dunkl Transform
We conjecture a geometrical form of the Paley–Wiener theorem for the Dunkl transform and prove three instances thereof, by using a reduction to the one-dimensional even case, shift operators, and a limit transition from Opdam’s results for the graded Hecke algebra, respectively. These Paley– Wiener theorems are used to extend Dunkl’s intertwining operator to arbitrary smooth functions. Furtherm...
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ژورنال
عنوان ژورنال: Journal d'Analyse Mathématique
سال: 2004
ISSN: 0021-7670,1565-8538
DOI: 10.1007/bf02787762