J. Korean Math. Soc. 2009; 46(2): 327-345
Printed March 1, 2009
Copyright © The Korean Mathematical Society.
Seung Jun Chang and Hyun Soo Chung
Dankook University
In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}$ to obtain a complete orthonormal set in $L_2(C_{a,b})$ where $C_{a,b}$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional $F$ in $L_2(C_{a,b})$ has a generalized Fourier-Wiener function space transform $\mathcal{F}_{\sqrt2,i}(F)$ also belonging to $L_2(C_{a,b})$.
Keywords: generalized Brownian motion process, generalized Hermite function, generalized Fourier-Hermite coefficient, generalized Fourier-Wiener function space transform
MSC numbers: 28C20, 60J65
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