Application of the dual space of Gelfand-Shilov spaces of Beurling type
Abstract
Using a previously obtained structure theorem of Gelfand-Shilov spaces $\Sigma _{\alpha }^{\beta }$ of Beurling type of ultradistributions, we prove that these ultradistributions can be represented as an initial values of solutions of the heat equation by describing the action of the Gauss-Weierstrass semigroup on the dual space $(\Sigma _{\alpha }^{\beta})^{\prime }.$
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References
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