Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions

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We give a simple proof of the Kernel theorem for the space of tempered ultradistributions of Beurling - Komatsu type, using the characterization of Fourier-Hermite coefficients of the elements of the space. We prove in details that the test space of tempered ultradistributions of Beurling - Komatsu type can be identified with the space of sequences of ultrapolynomal falloff and its dual space with the space of sequences of ultrapolynomial growth. As a consequence of the Kernel theorem we have that the Weyl transform can be extended on a space of tempered ultradistributions of Beurling - Komatsu type.
accepted for publication in Integral transforms and special functions

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Functional Analysis, Primary 46F05; Secondary 46F12, 42A16, 35S

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http://salesiana.dossiersoluciones.com/handle/123456789/123331

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702093
 http://arxiv.org/abs/math/0702093

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arXiv