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We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification B_C of an abstract Wiener space (H, B, v). Secondly, we introduce a new class of convolution products of functionals defined on B_C and study several properties of the convolutions. Then we study various relations among the first variation, the convolutions, and the generalized Fourier--Gauss transforms.
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참고문헌 (18)
참고문헌 신청
D. M. Chung / 1997 / Transforms on white noise functionals with their applications to Cauchy problems / Nagoya Math. J 147 : 1 ~ 23
D. M. Chung / 1998 / Transformation groups on white noise functionals and their applications / Appl. Math. Optim 37 (2) : 205 ~ 223
H. H. Kuo / 1975 / Gaussian Measures in Banach Spaces / Lecture Notes in Mathematics 463
H. H. Kuo / 1996 / White Noise Distribution Theory / CRC Press
I. Yoo / 1995 / Convolution and the Fourier-Wiener transform on abstract Wiener space / Rocky Mountain J. Math 25 (4) : 1577 ~ 1587
D. M. Chung / 1998 / Transformation groups on white noise functionals and their applications / Appl. Math. Optim 37 (2) : 205 ~ 223
H. H. Kuo / 1975 / Gaussian Measures in Banach Spaces / Lecture Notes in Mathematics 463
H. H. Kuo / 1996 / White Noise Distribution Theory / CRC Press
I. Yoo / 1995 / Convolution and the Fourier-Wiener transform on abstract Wiener space / Rocky Mountain J. Math 25 (4) : 1577 ~ 1587
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