Existence theorems and evaluation formulas for sequential Yeh-Feynman integrals
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Abstract
We establish the existence of the sequential Yeh-Feynman integral for functionals of the form
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References
[1] J. M. Ahn, K. S. Chang, and I. Yoo, "Some Banach algebras of Yeh-Feynman integrable functionals," J. Korean Math. Soc., vol. 24, pp. 257–266, 1987. Google Scholar
[2] E. Berkson and T. A. Gillespie, "Absolutely continuous functions of two variables and well-bounded operators," J. London Math. Soc., vol. 30, pp. 305–321, 1984. DOI: https://doi.org/10.1112/jlms/s2-30.2.305. Google Scholar
[3] R. H. Cameron and D. A. Storvick, "Some Banach algebras of analytic Feynman integrable functionals," Analytic Functions Kozubnik 1979, Lecture Notes in Mathematics, vol. 798, pp. 18–67, Springer-Verlag, Berlin, 1980. DOI: https://doi.org/10.1007/bfb0097256. Google Scholar
[4] R. H. Cameron and D. A. Storvick, "A simple definition of the Feynman integral, with applications," Mem. Amer. Math. Soc., No. 288, Amer. Math. Soc., 1983. DOI: https://doi.org/10.1090/memo/0288. Google Scholar
[5] R. H. Cameron and D. A. Storvick, "Sequential Fourier-Feynman transforms," Ann. Acad. Sci. Fenn., vol. 10, pp. 107–111, 1985. DOI: https://doi.org/10.5186/aasfm.1985.1013. Google Scholar
[6] R. H. Cameron and D. A. Storvick, "New existence theorems and evaluation formulas for sequential Feynman integrals," Proc. London Math. Soc., vol. 52, pp. 557–581, 1986. DOI: https://doi.org/10.1112/plms/s3-52.3.557. Google Scholar
[7] R. H. Cameron and D. A. Storvick, "New existence theorems and evaluation formulas for analytic Feynman integrals," Deformations Math. Struct., Complex Analy. Phys. Appl., Kluwer Acad. Publ., Dordrecht, pp. 297–308, 1989. DOI: https://doi.org/10.1007/978-94-009-2643-1_27. Google Scholar
[8] K. S. Chang, D. H. Cho, B. S. Kim, T. S. Song, and I. Yoo, "Sequential Fourier-Feynman transform, convolution and first variation," Trans. Amer. Math. Soc., vol. 360, pp. 1819–1838, 2008. DOI: https://doi.org/10.1090/S0002-9947-07-04383-8. Google Scholar
[9] K. S. Chang, J. G. Kim, and I. Yoo, "Relationships between the sequential Yeh-Feynman integral and Truman integral," Bull. Korean Math. Soc., vol. 24, pp. 173–180, 1987. Google Scholar
[10] K. S. Chang, J. G. Kim, I. Yoo, and K. S. Choi, "Sequential Yeh-Feynman integrals of certain classes of functionals," Commun. Korean Math. Soc., vol. 3, pp. 213–224, 1988. Google Scholar
[11] J. G. Choi, "Yeh-Fourier-Feynman transforms and convolutions associated with Gaussian processes," Ann. Funct. Anal., vol. 12, pp. 12–41, 2021. DOI: https://doi.org/10.1007/s43034-021-00128-7. Google Scholar
[12] B. S. Kim, "Integral transforms of square integrable functionals on Yeh-Wiener space," Kyungpook Math. J., vol. 40, pp. 155–166, 2009. DOI: https://doi.org/10.5666/KMJ.2009.49.1.155. Google Scholar
[13] B. S. Kim, "Generalized first variation and generalized sequential Fourier-Feynman transform," Korean J. Math., vol. 31, pp. 521–536, 2023. DOI: https://doi.org/10.11568/kjm.2023.31.4.521. Google Scholar
[14] B. S. Kim and Y. K. Yang, "Fourier-Yeh-Feynman transform and convolution on Yeh-Wiener space," Korean J. Math., vol. 16, pp. 335–348, 2008. Google Scholar
[15] B. S. Kim and I. Yoo, "Generalized sequential convolution product for the generalized sequential Fourier-Feynman transform," Korean J. Math., vol. 29, pp. 321–332, 2021. DOI: https://doi.org/10.11568/kjm.2021.29.2.321. Google Scholar
[16] J. Yeh, "Wiener measure in a space of functions of two variables," Trans. Amer. Math. Soc., vol. 95, pp. 433–450, 1960. DOI: https://doi.org/10.2307/1993566. Google Scholar
[17] J. Yeh, Stochastic processes and the Wiener integral, Marcel Dekker, New York, 1973. Google Scholar
[18] I. Yoo and B. S. Kim, "Generalized sequential Feynman integral and Fourier-Feynman transform," Rocky Mountain J. Math., vol. 51, pp. 2251–2268, 2021. DOI: https://doi.org/10.1216/rmj.2021.51.2251. Google Scholar