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In this paper, we define generalized Fourier-Hermite functionals on a function space C_(a,b)[0, T] to obtain a complete orthonormal set in L_2C_(a,b)[0, T] where C_(a,b)[0, T] is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in L_2C_(a,b)[0, T] has a generalized Fourier-Wiener function space transform F_{2^1/2,i}(F) also belonging to L_2C_(a,b)[0, T].
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참고문헌 (16)
참고문헌 신청
B. S. Kim / 2003 / Integral transforms of functionals in L2(C0[0, T]) / Rocky Mountain J. Math. 33 (4) : 1379 ~ 1393
D. Skoug / 2004 / A survey of results involving transforms and convolutions in function space / Rocky Mountain J. Math. 34 (3) : 1147 ~ 1175
E. Nelson / 1967 / Dynamical Theories of Brownian Motion (2nd edition), Math. Notes / Princeton University Press
J. Yeh / 1971 / Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments / Illinois J. Math. 15 : 37 ~ 46
J. Yeh / 1973 / Stochastic Processes and the Wiener Integral / Marcel Dekker, Inc.
D. Skoug / 2004 / A survey of results involving transforms and convolutions in function space / Rocky Mountain J. Math. 34 (3) : 1147 ~ 1175
E. Nelson / 1967 / Dynamical Theories of Brownian Motion (2nd edition), Math. Notes / Princeton University Press
J. Yeh / 1971 / Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments / Illinois J. Math. 15 : 37 ~ 46
J. Yeh / 1973 / Stochastic Processes and the Wiener Integral / Marcel Dekker, Inc.
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