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In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.
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참고문헌 (11)
참고문헌 신청
R. H. Cameron / 1968 / An operator-valued function space integral and a related integral equation / J. Math. Mech 18:517~552
R. H. Cameron / 1973 / An operator-valued function space integral applied to integrals of functions of class L1 / Proc. London Math. Soc. (3) 27:345~360
R. H. Cameron / 1980 / Some Banach algebras of analytic Feynman integrable functionals / Analytic functions, Kozubnik 1979 (Proc. Seventh Conf.) :18~67
D. H. Cho / 2008 / A simple formula for an analogue of conditional Wiener integrals and its applications / Trans. Amer. Math. Soc 360(7):3795~3811
D. H. Cho / 2010 / Operator-valued Feynman integral via conditional Feynman integrals on a func-tion space / Cent. Eur. J. Math 8(5):908~927
R. H. Cameron / 1973 / An operator-valued function space integral applied to integrals of functions of class L1 / Proc. London Math. Soc. (3) 27:345~360
R. H. Cameron / 1980 / Some Banach algebras of analytic Feynman integrable functionals / Analytic functions, Kozubnik 1979 (Proc. Seventh Conf.) :18~67
D. H. Cho / 2008 / A simple formula for an analogue of conditional Wiener integrals and its applications / Trans. Amer. Math. Soc 360(7):3795~3811
D. H. Cho / 2010 / Operator-valued Feynman integral via conditional Feynman integrals on a func-tion space / Cent. Eur. J. Math 8(5):908~927
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