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http://dx.doi.org/10.4134/JKMS.2009.46.2.327

GENERALIZED FOURIER-WIENER FUNCTION SPACE TRANSFORMS  

Chang, Seung-Jun (DEPARTMENT OF MATHEMATICS DANKOOK UNIVERSITY)
Chung, Hyun-Soo (DEPARTMENT OF MATHEMATICS DANKOOK UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.2, 2009 , pp. 327-345 More about this Journal
Abstract
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 $L_2(C_{a,b}[0,\;T])$ 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 $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.
Keywords
generalized Brownian motion process; generalized Hermite function; generalized Fourier-Hermite coefficient; generalized Fourier-Wiener function space transform;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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