대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제14권2호
  • /
  • Pages.329-336
  • /
  • 1999
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

WHITE NOISE HYPERFUNCTIONS

  • 발행 : 1999.04.01
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초록

We construct the Gelfand triple based on the space \ulcorner, introduced by Sato and di Silva, of analytic and exponentially decreasing function. This space denoted by(\ulcorner) of white noise test functionals are defined by the operator cosh \ulcorner, A=-(\ulcorner)\ulcorner+x\ulcorner+1. We also note that many properties like generalizations of the Paley-Wiener theorem and the Bochner-Schwartz theorem hold in this space as in the space of Hida distributions.

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참고문헌

  1. Publ. RIMS v.31 Distributions with exponential growth and Bochner-Schwartz theorem for Fourier hyperfunctions S.-Y. Chung;D. Kim
  2. Publ. RIMS v.30 A characterization for Fourier hyperfunctions J. Chung;S. -Y. Chung;D. Kim
  3. Nagoya Math. J. v.140 Positive definite hyperfunctions
  4. J. Fac. Sci. Univ. Tokyo, Sect. IA v.40 Solvability of Mizohata and Lewy operators S.-Y. Chung;D. Kim;S. K. Kim
  5. Japan. J. Math. v.19 Structure of the extended Fourier hyperfunctions
  6. White noise: An infinite dimensional calculus T. Hida;H.-H. Kuo;J. Potthoff;L. Streit
  7. Publ. RIMS v.29 Fourier hyperfunctions as the boundary values of smooth solutions of heat equations K. H. Kim;S.-Y. Chung;D. Kim
  8. Soochow J. Math. v.18 Lectures on white noise analysis H.-H. Kuo
  9. Lect. Notes in Math. v.1577 Elements of whithe noise calculus N. Obata