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Integral Transforms of Square Integrable Functionals on Yeh- Wiener Space

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경북대학교 자연과학대학 수학과|2009.03|Kyungpook Mathematical Journal|제49권 제1호|pp. 155-166

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참고문헌

키워드

integral transformYeh-Wiener integralFourier-Wiener transformFourier-Hermite functional
주제분류수학

초록

We give a necessary and sufficient condition that a square integrable func- tional F(x) on Yeh-Wiener space has an integral transform Fα,βF(x) which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in L2(C0[0, T]).

Abstract

We give a necessary and sufficient condition that a square integrable func- tional F(x) on Yeh-Wiener space has an integral transform Fα,βF(x) which is also square integrable. This extends the result by Kim and Skoug for functional F(x) in L2(C0[0, T]).

참고문헌 (16)

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  3. R. H. Cameron, "Fourier-Wiener transforms of analytic func-tionals", Duke Math. J, 12, pp.489~507 (1945)
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  10. B. J. Kim, "Integral transforms of functionals on a function space of two variables", ~, submitted
  11. ), "Rocky Mountain J. Math", 2003, 1379~1393
  12. Y. J. Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Funct. Anal, 47, pp.153~164 (1982)
  13. D. Skoug, "A survey of results involving transforms and convo-lutions in function space", Rocky Mountain J. Math, 34, pp.1147~1176 (2004)
  14. J. Yeh, "Wiener measure in a space of functions of two variables", Trans. Amer. Math. Soc, 95, pp.433~450 (1960)
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  16. J. Yeh, "Stochastic processes and the Wiener integral" (1983), Marcel Dekker

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