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Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions

Z. Lozanov-Crvenkovic·D. Perisic
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Abstract

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.

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Z. Lozanov-Crvenkovic, D. Perisic. 2007-02-05. Kernel theorem for the space of Beurling - Komatsu tempered ultradistibutions. https://arxiv.org/abs/math/0702093

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