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In this paper, we analyze the necessary and sufficient condition introduced in \cite{SJHSF}: 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.
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참고문헌 (21)
참고문헌 신청
R. H. Cameron / 1945 / Some examples of Fourier-Wiener transforms of analytic functionals / Duke Math. J 12:485~488
R. H. Cameron / 1945 / Fourier-Wiener transforms of analytic functionals / Duke Math. J 12:489~507
R. H. Cameron / 1947 / Fourier-Wiener transforms of functionals belonging to L2 over the space C / Duke Math. J 14:99~107
K. S. Chang / 2000 / Integral transforms and convolution of analytic functionals on abstract Wiener space / Numer. Funct. Anal. Optim 21(1-2):97~105
S. J. Chang / 2009 / Integral transforms of functionals in L 2(Ca,b[0, T]) / J. Fourier Anal. Appl 15(4):441~462
R. H. Cameron / 1945 / Fourier-Wiener transforms of analytic functionals / Duke Math. J 12:489~507
R. H. Cameron / 1947 / Fourier-Wiener transforms of functionals belonging to L2 over the space C / Duke Math. J 14:99~107
K. S. Chang / 2000 / Integral transforms and convolution of analytic functionals on abstract Wiener space / Numer. Funct. Anal. Optim 21(1-2):97~105
S. J. Chang / 2009 / Integral transforms of functionals in L 2(Ca,b[0, T]) / J. Fourier Anal. Appl 15(4):441~462
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