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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Fractional calculus and regularized residue of infinite dimensional space
verfasst von : Asada Akira
Erschienen in: Mathematical Methods in Engineering
Verlag: Springer Netherlands
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We have proposed regularization of infinite dimensional integral via fractional calculus. It is done on a Hilbert space H equipped with a Schatten class operator G. The
ζ
-function
ζ
(
G, s
) of G is assumed to be holomorphic at
s
=0. Regularization is done by using
ζ
(
G, s
). After reviewing this regularization, it is shown regularized Cauchy kernel of a Hilbert space with the determinant bundle exists if and only if
v
=
ζ
(
G
, 0) is an integer. Regularized residue on an infinite dimensional space is obtained as an application of regularized Cauchy kernel.