Growth properties of Paley-Wiener functions on Cn
نویسندگان
چکیده
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.
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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.
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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...
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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 کاملA spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on Cn
— We prove a spectral Paley-Wiener theorem for the Heisenberg group by means of a support theorem for the twisted spherical means on Cn. If f(z)e 1 4 |z| 2 is a Schwartz class function we show that f is supported in a ball of radius B in Cn if and only if f×μr(z) = 0 for r > B+ |z| for all z ∈ Cn. This is an analogue of Helgason’s support theorem on Euclidean and hyperbolic spaces. When n = 1 w...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1984
ISSN: 1385-7258
DOI: 10.1016/1385-7258(84)90061-1