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

Kim, Kwang-Whoi

  • Published : 2004.10.01

Abstract

We research properties of the space of measurable functions square integrable with weight exp$2\nu $\mid$x$\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 $C^n$ which are estimated with the aid of a special exponential function exp($\mu$|x|).

Keywords

Fourier hyperfunction;Fourier(-Laplace) operator;pseudodifferential operator;a countably Hilbert space;Sovolev′s embedding theorem;inductive(projective) limit

References

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  2. New spaces of functions and hyperfunctions for Hankel transforms and convolutions vol.153, pp.2, 2008, https://doi.org/10.1007/s00605-007-0498-9