[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.j150485

SOME EXPRESSIONS FOR THE INVERSE INTEGRAL TRANSFORM VIA THE TRANSLATION THEOREM ON FUNCTION SPACE

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.53, no.6, 2016 , pp. 1261-1273 More about this Journal

Abstract

In this paper, we analyze the necessary and sufficient condition introduced in [5]: that a functional F in $$L^2(C_{a,b}[0,T$ $]$ $)$$ has an integral transform ${\mathcal{F}}_{{\gamma},{\beta}}F$ , also belonging to $$L^2(C_{a,b}[0,T$ $]$ $)$$ . We then establish the inverse integral transforms of the functionals in $$L^2(C_{a,b}[0,T$ $]$ $)$$ and then examine various properties with respect to the inverse integral transforms via the translation theorem. Several possible outcomes are presented as remarks. Our approach is a new method to solve some difficulties with respect to the inverse integral transform.

Keywords

generalized Brownian motion process; generalized integral transform; dense subset; inverse integral transform; translation theorem;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
Cited By KSCI

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