• 제목/요약/키워드: extended Fourier hyperfunction

검색결과 3건 처리시간 0.021초

CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS

  • KIM KWANG WHOI
    • 대한수학회지
    • /
    • 제42권3호
    • /
    • pp.599-619
    • /
    • 2005
  • We define the convolutions of Fourier hyperfunctions and show that every strongly decreasing Fourier hyperfunction is a convolutor for the space of Fourier hyperfunctions and the converse is true. Also we show that there are no differential operator with constant coefficients which have a fundamental solution in the space of strongly decreasing Fourier hyperfunctions. Lastly we show that the space of multipliers for the space of Fourier hyperfunctions consists of analytic functions extended to any strip in $\mathbb{C}^n$ which are estimated with a special exponential function exp$(\mu|\chi|)$.

DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Kim, Kwang-Whoi
    • 대한수학회보
    • /
    • 제41권4호
    • /
    • pp.785-803
    • /
    • 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.

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

  • Kim, Kwang-Whoi
    • 대한수학회논문집
    • /
    • 제19권4호
    • /
    • pp.661-681
    • /
    • 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|).