• 제목/요약/키워드: hyperfunctions

검색결과 13건 처리시간 0.02초

CONVOLUTORS FOR THE SPACE OF FOURIER HYPERFUNCTIONS

  • KIM KWANG WHOI
    • 대한수학회지
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    • 제42권3호
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    • pp.599-619
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    • 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$(\mu|\chi|)$.

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

  • Kim, Kwang-Whoi
    • 대한수학회논문집
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    • 제19권4호
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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|).

HYERS-ULAM-RASSIAS STABILITY OF QUADRATIC FUNCTIONAL EQUATION IN THE SPACE OF SCHWARTZ TEMPERED DISTRIBUTIONS

  • CHUNG JAEYOUNG
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제12권2호
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    • pp.133-142
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    • 2005
  • Generalizing the Cauchy-Rassias inequality in [Th. M. Rassias: On the stability of the linear mapping in Banach spaces. Proc. Amer. Math. Soc. 72 (1978), no. 2, 297-300.] we consider a stability problem of quadratic functional equation in the spaces of generalized functions such as the Schwartz tempered distributions and Sato hyperfunctions.

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DENSENESS OF TEST FUNCTIONS IN THE SPACE OF EXTENDED FOURIER HYPERFUNCTIONS

  • Kim, Kwang-Whoi
    • 대한수학회보
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    • 제41권4호
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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.

REPRESENTATION OF THE GENERALIZED FUNCTIONS OF GELFAND AND SHILOV

  • Jae Young Chung;Sung Jin Lee
    • 대한수학회논문집
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    • 제9권3호
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    • pp.607-616
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    • 1994
  • I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to investigate the uniqueness of the solutions of the Cauchy problems of partial differential equations. Using the heat kernel method Matsuzawa gave structure theorems for distributions, hyperfunctions and generalized functions in the dual space $(S^s_r)'$ of the Gelfand-Shilov space of type S in [M1, M2 and DM], respectively. Also, we gave structure theorems for ultradistributions, Fourier hyperfunctions in [CK, KCK], respectively.

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BOCHNER-SCHWARTZ THEOREM ON LOCALLY COMPACT ABELIAN GROUPS

  • Kim, Jin-Man;Cho, Jong-Gyu
    • 대한수학회보
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    • 제38권1호
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    • pp.7-16
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    • 2001
  • We study the Fourier transformation on the Gelfand-Bruhat space of type S and characterize this space by means of Fourier transform on a locally compact abelian group G. Also, we extend Bochner-Schwartz theorem to the dual space of the Gelfand-Bruhat space and the space of Fourier hyperfunctions on G. respectively.

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GLOBAL UNIQUENESS FOR THE RADON TRANSFORM

  • Takiguchi, Takashi
    • 대한수학회보
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    • 제57권3호
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    • pp.597-605
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    • 2020
  • In this article, we discuss the global uniqueness problem for the Radon transform. It is not sufficient for the global uniqueness for the Radon transform to assume that the Radon transform Rf for a function f absolutely converges on any hyperplane. It is also known that it is sufficient to assume that f ∈ L1 for the global uniqueness to hold. There exists a big gap between the above two conditions, to fill which is our purpose in this paper. We shall give a better sufficient condition for the global uniqueness of the Radon transform.