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http://dx.doi.org/10.14403/jcms.2010.23.2.349

INTEGRAL TRANSFORMS OF FUNCTIONALS ON A FUNCTION SPACE OF TWO VARIABLES  

Kim, Bong Jin (Department of Mathematics Daejin University)
Kim, Byoung Soo (School of Liberal Arts Seoul National University of Technology)
Yoo, Il (Department of Mathematics Yonsei University)
Publication Information
Journal of the Chungcheong Mathematical Society / v.23, no.2, 2010 , pp. 349-362 More about this Journal
Abstract
We establish the various relationships among the integral transform ${\mathcal{F}}_{{\alpha},{\beta}}F$, the convolution product $(F*G)_{\alpha}$ and the first variation ${\delta}F$ for a class of functionals defined on K(Q), the space of complex-valued continuous functions on $Q=[0,S]{\times}[0,T]$ which satisfy x(s, 0) = x(0, t) = 0 for all $(s,t){\in}Q$. And also we obtain Parseval's and Plancherel's relations for the integral transform of some functionals defined on K(Q).
Keywords
Yeh-Wiener integral; integral transform; convolution product; first variation; Parseval's relation; Plancherel's relation;
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