QUASIANALYTIC FUNCTION CLASSES AND THE COMPLEX-TIME DIFFUSION GROUP - I
Copyright policy )QUASIANALYTIC FUNCTION CLASSES AND THE COMPLEX-TIME DIFFUSION GROUP - I
In this paper necessary and sufficient conditions are given for quasianalytic function classes D({Mk}) and the corresponding classes of distributions D′({Mk}) to be invariant with respect to the diffusion group Ut where −∞<t<∞. In addition, the properties of hyperdistributions [Formula: see text] are studied, where δ0 denotes the δ-function at 0. It is shown that hyperdistributions Γ from the class D′({Mk}) are completely characterized by the rate of decay of the moments μk(Γ) = Γ(xk), k≥0.
- Boston College United States
- Boston University United States
quasianalytic function classes, diffusion group, hyperdistributions, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, invariant, Topological linear spaces of test functions, distributions and ultradistributions, rate of decay of the moments, Quasi-analytic and other classes of functions of one complex variable, classes of distributions
quasianalytic function classes, diffusion group, hyperdistributions, Banach algebras of differentiable or analytic functions, \(H^p\)-spaces, invariant, Topological linear spaces of test functions, distributions and ultradistributions, rate of decay of the moments, Quasi-analytic and other classes of functions of one complex variable, classes of distributions
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