On some extension of Paley Wiener theorem

IF 0.3 Q4 MATHEMATICS Concrete Operators Pub Date : 2020-01-01 DOI:10.1515/conop-2020-0006
Ettien Yves-Fernand N’Da, K. Kangni
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引用次数: 0

Abstract

Abstract Paley Wiener theorem characterizes the class of functions which are Fourier transforms of ℂ∞ functions of compact support on ℝn by relating decay properties of those functions or distributions at infinity with analyticity of their Fourier transform. The theorem is already proved in classical case : the real case with holomorphic Fourier transform on L2(ℝ), the case of functions with compact support on ℝn from Hörmander and the spherical transform on semi simple Lie groups with Gangolli theorem. Let G be a locally compact unimodular group, K a compact subgroup of G, and δ an element of unitary dual ̑K of K. In this work, we’ll give an extension of Paley-Wiener theorem with respect to δ, a class of unitary irreducible representation of K, where G is either a semi-simple Lie group or a reductive Lie group with nonempty discrete series after introducing a notion of δ-orbital integral. If δ is trivial and one dimensional, we obtain the classical Paley-Wiener theorem.
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关于佩利维纳定理的推广
摘要Paley-Wiener定理刻画了一类函数,这些函数是ℂ∞ 上的紧凑型支撑功能ℝ通过将这些函数或分布在无穷大处的衰变性质与它们的傅立叶变换的分析性联系起来。该定理已经在经典情况下得到证明:L2上全纯傅立叶变换的真实情况(ℝ), 上具有紧凑支持的函数的情况ℝn和Gangolli定理的半单李群上的球面变换。设G是局部紧幺模群,K是G的紧子群,δ是K的酉对偶̑K的一个元素,在引入δ-轨道积分概念后,G是半单李群或具有非空离散级数的约化李群。如果δ是平凡的并且是一维的,我们得到了经典的帕利-维纳定理。
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来源期刊
Concrete Operators
Concrete Operators MATHEMATICS-
CiteScore
1.00
自引率
16.70%
发文量
10
审稿时长
22 weeks
期刊最新文献
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