Kernel Theorem for the Space of Beurling - Komatsu Tempered Ultradistibutions
نویسنده
چکیده
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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