Asymptotic Fourier and Laplace transformations for hyperfunctions

• Autorzy: Michael Langenbruch
• Języki publikacji: EN

Abstrakty

EN

We develop an elementary theory of Fourier and Laplace transformations for exponentially decreasing hyperfunctions. Since any hyperfunction can be extended to an exponentially decreasing hyperfunction, this provides simple notions of asymptotic Fourier and Laplace transformations for hyperfunctions, improving the existing models. This is used to prove criteria for the uniqueness and solvability of the abstract Cauchy problem in Fréchet spaces.

Kategorie tematyczne

• 42A38: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
• 44A10: Laplace transform
• 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
• 46F15: Hyperfunctions, analytic functionals
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 205
• Numer: 1
• Strony: 41-69

Daty

wydano

2011

Twórcy

autor

Michael Langenbruch

• Department of Mathematics, University of Oldenburg, D-26111 Oldenburg, Germany

Identyfikatory

DOI

10.4064/sm205-1-4