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Joint Eigenfunctions On The Heisenberg Group And Support Theorems On Rn

Electronic Theses of Indian Institute of Science

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Field Value
 
Title Joint Eigenfunctions On The Heisenberg Group And Support Theorems On Rn
 
Creator Samanta, Amit
 
Subject Harmonic Analysis
Hecke-Bochner Identity
Heisenberg Group
Convolution Equations
Eigenfunctions
K-Spherical Functions
Differential Operators
Weyl Transform
Recursion Theory
Mathematics
 
Description This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively.
Let Hn be the (2n + 1)-dimensional Heisenberg group, and let K be a compact subgroup of U(n), such that (K, Hn) is a Gelfand pair. Also assume that the K-action on Cn is polar. We prove a Hecke-Bochner identity associated to the Gelfand pair (K, Hn). For the special case K = U(n), this was proved by Geller, giving a formula for the Weyl transform of a function f of the type f = Pg, where g is a radial function, and P a bigraded solid U(n)-harmonic polynomial. Using our general Hecke-Bochner identity we also characterize (under some conditions) joint eigenfunctions of all differential operators on Hn that are invariant under the action of K and the left action of Hn .
We consider convolution equations of the type f * T = g, where f, g ε Lp(Rn) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T , we show that f is compactly supported, provided g is.
 
Contributor Narayanan, E K
 
Date 2014-04-07T10:26:00Z
2014-04-07T10:26:00Z
2014-04-07
2012-05
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2289
http://etd.ncsi.iisc.ernet.in/abstracts/2947/G25274-Abs.pdf
 
Language en_US
 
Relation G25274