Mapping properties for the Bargmann transform on modulation spaces
Journal article, Peer reviewed
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Original versionSignahl, M., & Toft, J. (2012). Mapping properties for the Bargmann transform on modulation spaces. Journal of Pseudo-Differential Operators and Applications, 3(1), 1-30. doi: 10.1007/s11868-011-0039-0
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions. We also present some consequences. For example we prove that the spectrum of the Harmonic oscillator is the same for all modulation spaces.
Published version of an article published in the journal: Journal of Pseudo-Differential Operators and Applications. Also available from the publisher at: http://dx.doi.org/10.1007/s11868-011-0039-0