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A New Analytic Fourier-Feynman Transform w.r.t. Subordinate Brownian Motion
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In this paper, we first introduce a new Lp analytic Fourier Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L p -AFFTSB, the convolution product, and the gradient operator for several types of functionals.
Abstract
In this paper, we first introduce a new Lp analytic Fourier Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L p -AFFTSB, the convolution product, and the gradient operator for several types of functionals.
참고문헌 (13)
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- S.J. Chang, "Generalized Fourier-Feynman transforms, convo-lution products, and first variations on function space", Rocky Mountain J. Math., 40, pp.761~788 (2010)
- S. J. Chang, "Integration by parts formulas involving generalized Fourier-Feynman transforms on function space", Trans. Amer. Math. Soc, 355, pp.2925~2948 (2003)
- S.J. Chang, "Rotation of Gaussian paths on Wiener space with applications", Banach J. Math. Anal, 12, pp.651~672 (2018)
- S.J. Chang, "A new approach method to obtain the L1 general-ized analytic Fourier-Feynman transform", Integral Transforms Spec. Funct, 29, pp.745~760 (2018)
- C.S. Deng, "On a Cameron-Martin type quasi-invariance theorem and applications to subordinate Brownian motion", Stoch. Anal. Appl, 33, pp.975~993 (2015)
- G.W. Johnson, "An Lp analytic Fourier-Feynman transform", Michigan Math. J, 26, pp.103~127 (1979)
- J.G. Kim, "Relationships among transforms, convolutions, and first variations", Int. J. Math. Math. Sci, 22, pp.191~204 (1999)
- D. Skoug, "A survey of results involving transforms and convolutions in function space", Rocky Mountain J. Math, 34, pp.1147~1175 (2004)
- R. L. Schilling, "De Gruyter Studies in Mathematics", pp.37~ (2012), Walter de Gruyter & Co
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