Generalized Cameron-Storvick type theorem via the bounded linear operators
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.
Abstract
In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.
참고문헌 (24)
- R. H. Cameron, "Transformations of Wiener integrals under transla-tions", Ann. of Math, 45, pp.386~396 (1944)[DOI]
- R. H. Cameron, "The orthogonal development of non-linear functionals in series of Fourier-Hermite functionals", Ann. of Math, 48(2), pp.385~392 (1947)[DOI]
- S. J. Chang, "Translation theorem for function space integral associated with Gaussian paths and applications", Bull. Iranian Math. Soc
- S. J. Chang, "Evaluation formulas for conditional function space integrals", I, Stoch. Anal. Appl., 25(1), pp.141~168 (2007)[DOI]
- S. J. Chang, "Conditional function space integrals with applications", Rocky Mountain J. Math, 26(1), pp.37~62 (1996)[DOI]
- 장승준, "Some expressions for the inverse integral transform via the translation theorem on function space", 대한수학회지, 53(6), pp.1261~1273 (2016), 대한수학회
- ), "J. Fourier Anal. Appl", 2009, 441~462, https:
- S. J. Chang, "Some basic relationships among transforms, convolution products, rst varia-tions and inverse transforms", Cent. Eur. J. Math, 11(3), pp.538~551 (2013)[DOI]
- K. S. Chang, "Integral transform and convolution of analytic functionals on abstract Wiener space", Numer. Funct. Anal. Optim., 21(1-2), pp.97~105 (2000)[DOI]
- S. J. Chang, "Generalized Fourier-Feynman transforms and a rst vari-ation on function space", Integral Transforms Spec. Funct, 14(5), pp.375~393 (2003)[DOI]
- S. J. Chang, "Relationships for modied generalized integral transforms, modied convolution products and rst variations on function space, Inte-gral Transforms Spec", Funct, 25(10), pp.790~804 (2014)[DOI]
- D. M. Chung, "Transforms on white noise functionals with their applications to Cauchy problems", Nagoya Math. J, 147, pp.1~23 (1997)[DOI]
- H. S. Chung, "Generalized integral transforms and convolution products on function space", Integral Transforms Spec. Funct, 22(8), pp.573~586 (2011)[DOI]
- L. Gross, "Abstract Wiener spaces", Proc. Fifth Berkeley Sympos. Math. Statist. and Probability, 2, pp.31~42 (1967), California Press
- 임만규, "Relations among the first variation, the convolutions and the generalized Fourier-Gauss transforms", 대한수학회보, 48(2), pp.291~302 (2011), 대한수학회
- B. J. Kim, "Conditional integral transforms, conditional convolution products and rst variations for some conditioning functions", Far East J. Math. Sci. (FJMS), 19(3), pp.245~258 (2005)
- 김봉진, "PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE", 한국수학논문집, 22(1), pp.57~69 (2014), 강원경기수학회[DOI]
- B. J. Kim, "Conditional integral transforms, conditional con-volution products and rst variations", Pan Amer. Math. J., 14(3), pp.27~47 (2004)
- ), "Rocky Mountain J. Math", 2003, 1379~1393, https:
- H. H. Kuo, "Gaussian Measures in Banach Spaces", Lecture Notes in Mathematics, 463 (1975), Springer-Verlag
- Y. J. Lee, "Integral transforms of analytic functions on abstract Wiener spaces", J. Func-tional Analysis, 47(2), pp.153~164 (1982)[DOI]
- E. Nelson, "Dynamical Theories of Brownian Motion" (1967), Princeton University Press
- J. Yeh, "Singularity of Gaussian measures on function spaces induced by Brownian motion processes with non-stationary increments", Illinois J. Math, 15, pp.37~46 (1971)
- J. Yeh, "Stochastic Processes and the Wiener Integral" (1973), Marcel Dekker, #Inc