The Bargmann transform and powers of harmonic oscillator on Gelfand-Shilov subspaces

2015/07/17 by Carmen Fernández, Carmen Fernandez, Antonio Galbis +4
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Boundary Problems #Mathematical Analysis and Transform Methods #math.FA

paper · pdf · doi:10.48550/arxiv.1507.04850

14 pages

arxiv created 2015/07/17 · arxiv updated 2015/07/20

Abstract

We consider the counter images \maclJ (\rr d) and \maclJ ₀(\rr d) of entire functions with exponential and almost exponential bounds, respectively, under the Bargmann transform, and we characterize them by estimates of powers of the harmonic oscillator. We also consider the Pilipović spaces \bsycalS _s(\rr d) and \bsySig _s(\rr d) when 0<s<1/2 and deduce their images under the Bargmann transform.

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