Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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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)
  • Received : 2010.04.02
  • Accepted : 2010.06.01
  • Published : 2010.06.30
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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).

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References

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