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The Taylor transformation of analytic functionals with non-bounded carrier

Grzegorz Łysik — 1994

Studia Mathematica

Let L be a closed convex subset of some proper cone in ℂ. The image of the space of analytic functionals Q'(L) with non-bounded carrier in L under the Taylor transformation as well as the representation of analytic functionals from Q'(L) as the boundary values of holomorphic functions outside L are given. Multipliers and operators in Q'(L) are described.

A Phragmén-Lindelöf type quasi-analyticity principle

Grzegorz Łysik — 1997

Studia Mathematica

Quasi-analyticity theorems of Phragmén-Lindelöf type for holomorphic functions of exponential type on a half plane are stated and proved. Spaces of Laplace distributions (ultradistributions) on ℝ are studied and their boundary value representation is given. A generalization of the Painlevé theorem is proved.

Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation

Todor GramchevGrzegorz Łysik — 2008

Banach Center Publications

We study the Gevrey regularity down to t = 0 of solutions to the initial value problem for a semilinear heat equation t u - Δ u = u M . The approach is based on suitable iterative fixed point methods in L p based Banach spaces with anisotropic Gevrey norms with respect to the time and the space variables. We also construct explicit solutions uniformly analytic in t ≥ 0 and x ∈ ℝⁿ for some conservative nonlinear terms with symmetries.

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