THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES

Title & Authors
THE SPACE OF FOURIER HYPERFUNCTIONS AS AN INDUCTIVE LIMIT OF HILBERT SPACES
Kim, Kwang-Whoi;

Abstract
We research properties of the space of measurable functions square integrable with weight exp$2\nu $\small{\mid}$x$\small{\mid}$$, and those of the space of Fourier hyperfunctions. Also we show that the several embedding theorems hold true, and that the Fourier-Lapace operator is an isomorphism of the space of strongly decreasing Fourier hyperfunctions onto the space of analytic functions extended to any strip in $\small{C^n}$ which are estimated with the aid of a special exponential function exp($\small{\mu}$｜x｜).
Keywords
Fourier hyperfunction;Fourier(-Laplace) operator;pseudodifferential operator;a countably Hilbert space;Sovolev′s embedding theorem;inductive(projective) limit;
Language
English
Cited by
1.
Abstract Volterra Integro-Differential Equations: Approximation and Convergence of Resolvent Operator Families, Numerical Functional Analysis and Optimization, 2014, 35, 12, 1579
2.
New spaces of functions and hyperfunctions for Hankel transforms and convolutions, Monatshefte für Mathematik, 2008, 153, 2, 89
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