Integral Transforms of Functionals in L 2(C a,b [0,T])

被引：31
|
作者：
Chang, Seung Jun [1 ]
Chung, Hyun Soo [1 ]
Skoug, David [2 ]
机构：
[1] Dankook Univ, Dept Math, Cheonan 330714, South Korea
[2] Univ Nebraska, Dept Math, Lincoln, NE 68588 USA
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2009年 / 15卷 / 04期
关键词：
Generalized Brownian motion process; Generalized Fourier-Hermite functionals; Integral transforms; FOURIER-FEYNMAN TRANSFORMS; FUNCTION-SPACE;
D O I：
10.1007/s00041-009-9076-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we use generalized Fourier-Hermite functionals 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 an integral transform F (gamma,beta) F also belonging to L (2)(C (a,b) [0,T]).
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页码：441 / 462
页数：22
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