Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지

A simple proof of analytic characterization theorem for operator symbols

  • Chung, Dong-Myung (Department of Mathematics, Sogang University, Seoul 121-742) ;
  • Chung, Tae-Su (Department of Mathematics, Sogang University, Seoul 121-742) ;
  • Ji, Un-Cig (Natural Science Institute, Yonsei University)
  • Published : 1997.08.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we first give a simple proof of the analytic characterization theorems of the operator symbols by using the characterization theorem for white noise functionals. We next give a criterion for the convergence of operators on white noise functionals in terms of their symbols and then use this result to give a proof for the Fock expansion theorem of operators on white noise functionals.

Keywords

References

  1. Carleton Math. Lect. Notes v.13 Analysis of Brownian functionals T. Hida
  2. White Noise: An Infinite Dimensional Calculus T. Hida;H.­H.Kuo;J. Potthoff;L. Streit
  3. Exploring Stochastic Laws, Festschrift in Honor of the 70th Birthday of V. S. Korolyuk A simple proof of Hida distribution characterization theorem I. Kubo;H.­H.Kuo;A. V. Skorokhod(ed.);Yu. V. Borovskikh (ed.)
  4. White noise distribution theory H.­H.Kuo
  5. Nagoya Math. J. v.121 A characterization of white noise test functionals H.­H. Kuo;J. Potthoff;L. Streit
  6. J. Math. Soc. Japan v.45 An analytic characterization of symbols of operators on white noise functionals N. Obata
  7. Lect. Notes in Math. v.1577 White Noise Calculus and Fock Space N. Obata
  8. J. Funct. Anal. v.101 A characterization of Hida distributions J. Potthoff;L. Streit