A change of scale formula for Wiener integrals of cylinder functions on abstract Wiener space.
Kim, Young Sik (1998)
International Journal of Mathematics and Mathematical Sciences
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Kim, Young Sik (1998)
International Journal of Mathematics and Mathematical Sciences
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Chang, Seung Jun, Kang, Soon Ja, Skoug, David (2000)
International Journal of Mathematics and Mathematical Sciences
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Dong Cho (2010)
Open Mathematics
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Let C 0r [0; t] denote the analogue of the r-dimensional Wiener space, define X t: C r[0; t] → ℝ2r by X t (x) = (x(0); x(t)). In this paper, we introduce a simple formula for the conditional expectations with the conditioning function X t. Using this formula, we evaluate the conditional analytic Feynman integral for the functional , where η is a complex Borel measure on [0, t], and θ(s, ·) and φ are the Fourier-Stieltjes transforms of the complex Borel measures on ℝr. We then introduce...
Skoug, D.L. (1974)
Portugaliae mathematica
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Chang, Seung Jun, Choi, Jae Gil (2002)
International Journal of Mathematics and Mathematical Sciences
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Ta Lê Loi (1995)
Annales de l'institut Fourier
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We consider some variants of Łojasiewicz inequalities for the class of subsets of Euclidean spaces definable from addition, multiplication and exponentiation : Łojasiewicz-type inequalities, global Łojasiewicz inequalities with or without parameters. The rationality of Łojasiewicz’s exponents for this class is also proved.
Angus Macintyre, David Marker (1997)
Revista Matemática de la Universidad Complutense de Madrid
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We show that log is needed to eliminate quantifiers in the theory of the real numbers with restricted analytic functions and exponentiation.
David Elworthy, Aubrey Truman (1984)
Annales de l'I.H.P. Physique théorique
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Sousa Pinto, J. (1993)
Portugaliae mathematica
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Byoung Kim, Il Yoo, Dong Cho (2010)
Open Mathematics
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Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class A1,A2 than the Fresnel class (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space...