Hermite expansions and Hardy's theorem

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dc.creatorVemuri, M. K.
dc.date2008-01-15
dc.date.accessioned2026-07-07T08:54:32Z
dc.date.available2026-07-07T08:54:32Z
dc.descriptionAssuming that both a function and its Fourier transform are dominated by a Gaussian of large variance, it is shown that the Hermite coefficients of the function decay exponentially. A sharp estimate for the rate of exponential decay is obtained in terms of the variance, and in the limiting case (when the variance becomes so small that the Gaussian is its own Fourier transform), Hardy's theorem on Fourier transform pairs is obtained. A quantitative result on the confinement of particle-like states of a quantum harmonic oscillator is obtained. A stronger form of the result is conjectured. Further, it is shown how Hardy's theorem may be derived from a weak version of confinement without using complex analysis.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/0801.2234
dc.identifierhttp://arxiv.org/abs/0801.2234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145967
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subjectRepresentation Theory
dc.subject35Q40
dc.titleHermite expansions and Hardy's theorem
dc.typetext

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