• Title, Summary, Keyword: projective(inductive) limit

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

  • Kim, Kwang-Whoi
    • Communications of the Korean Mathematical Society
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    • v.19 no.4
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    • pp.661-681
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    • 2004
  • 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|).

DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Kim, Kwang-Whoi
    • Bulletin of the Korean Mathematical Society
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    • v.41 no.4
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    • pp.785-803
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    • 2004
  • We research properties of analytic functions which are exponentially decreasing or increasing. Also we show that the space of test functions is dense in the space of extended Fourier hyper-functions, and that the Fourier transform of the space of extended Fourier hyperfunctions into itself is an isomorphism and Parseval's inequality holds.