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dc.contributor.advisorNarayanan, E K
dc.contributor.authorSamanta, Amit
dc.date.accessioned2014-04-07T10:26:00Z
dc.date.accessioned2018-07-31T06:08:58Z
dc.date.available2014-04-07T10:26:00Z
dc.date.available2018-07-31T06:08:58Z
dc.date.issued2014-04-07
dc.date.submitted2012
dc.identifier.urihttp://etd.iisc.ac.in/handle/2005/2289
dc.identifier.abstracthttp://etd.iisc.ac.in/static/etd/abstracts/2947/G25274-Abs.pdfen_US
dc.description.abstractThis 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.en_US
dc.language.isoen_USen_US
dc.relation.ispartofseriesG25274en_US
dc.subjectHarmonic Analysisen_US
dc.subjectHecke-Bochner Identityen_US
dc.subjectHeisenberg Groupen_US
dc.subjectConvolution Equationsen_US
dc.subjectEigenfunctionsen_US
dc.subjectK-Spherical Functionsen_US
dc.subjectDifferential Operatorsen_US
dc.subjectWeyl Transformen_US
dc.subjectRecursion Theoryen_US
dc.subject.classificationMathematicsen_US
dc.titleJoint Eigenfunctions On The Heisenberg Group And Support Theorems On Rnen_US
dc.typeThesisen_US
dc.degree.namePhDen_US
dc.degree.levelDoctoralen_US
dc.degree.disciplineFaculty of Scienceen_US


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