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Conditional Fourier-Feynman transform and conditional convolution product associated with vector-valued conditioning function

최재길|고애영
한국수학교육학회|2023.05|이론수학과 교직수학 (Theoretical Mathematics and Pedagogical Mathematics)|제30권 제2호|pp. 155-167|DOI https://doi.org/10.7468/jksmeb.2023.30.2.155

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키워드

Wiener spaceconditional convolution productconditional Fourier-Feynman transformPaley-Wiener-Zygmund stochastic integral.
주제분류수학

초록

In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functionals which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

Abstract

In this paper, we use a vector-valued conditioning function to define a conditional Fourier-Feynman transform (CFFT) and a conditional convolution product (CCP) on the Wiener space. We establish the existences of the CFFT and the CCP for bounded functionals which form a Banach algebra. We then provide fundamental relationships between the CFFTs and the CCPs.

참고문헌 (13)

  1. R.H. Cameron, "Some Banach algebras of analytic Feynman integrable functionals. Analytic Functions (Kozubnik 1979)", pp.18~67 (1979), Springer
  2. Dong Chung, "Scale-invariant measurability in abstract Wiener spaces", Pacific Journal of Mathematics, 130(1), pp.27~40 (1987), Mathematical Sciences Publishers[DOI]
  3. K.S. Chang, "Functions in the Banach algebra S(v)", J. Korean Math. Soc, 24, pp.151~158 (1987)
  4. Dong Myung Chung, "Generalized Feynman integrals via conditional Feynman integrals.", Michigan Mathematical Journal, 40(2), pp.377~391 (1993), Michigan Mathematical Journal[DOI]
  5. Dong Myung Chung, "Conditional Analytic Feynman Integrals and a Related Schrödinger Integral Equation", SIAM Journal on Mathematical Analysis, 20(4), pp.950~965 (1989), Society for Industrial & Applied Mathematics (SIAM)[DOI]
  6. R. E. A. C. Paley, "Notes on random functions", Mathematische Zeitschrift, 37(1), pp.647~668 (1933), Springer Science and Business Media LLC[DOI]
  7. Chull Park, "A Generalized Paley-Wiener-Zygmund Integral and Its Applications", Proceedings of the American Mathematical Society, 23(2), pp.388~400 (1969), JSTOR[DOI]
  8. Chull Park, "A Note on Paley-Wiener-Zygmund Stochastic Integrals", Proceedings of the American Mathematical Society, 103(2), pp.591~601 (1988), JSTOR[DOI]
  9. Chull Park, "A simple formula for conditional Wiener integrals with applications", Pacific Journal of Mathematics, 135(2), pp.381~394 (1988), Mathematical Sciences Publishers[DOI]
  10. Chull Park, "Conditional Wiener integrals. II", Pacific Journal of Mathematics, 167(2), pp.293~312 (1995), Mathematical Sciences Publishers[DOI]
  11. C. Park, "Conditional Fourier-Feynman transforms and conditional convo-lution products", J. Korean Math. Soc, 38, pp.61~76 (2001)
  12. H.G. Tucker, "A Graduate Course in Probability" (1967), Academic Press
  13. James Yeh, "Inversion of conditional Wiener integrals", Pacific Journal of Mathematics, 59(2), pp.623~638 (1975), Mathematical Sciences Publishers[DOI]

관련 논문AI추천

CONDITIONAL FOURIER–FEYNMAN TRANSFORM AND CONDITIONAL CONVOLUTION PRODUCT ASSOCIATED WITH INFINITE DIMENSIONAL CONDITIONING FUNCTION심상길, 최재길대한수학회 · 대한수학회보2023 · 제60권 제5호Conditional Fourier-Feynman transforms and convolutions of unbounded functions on a generalized Wiener space조동현대한수학회 · 대한수학회지2013 · 제50권 제5호Conditional Foruier-Feynman transform and convolution product for a vector valued conditioning function김봉진강원경기수학회 · 한국수학논문집2022 · 제30권 제2호Conditional generalized Fourier-Feynman transform and conditional convolution product on a Banach algebra장승준, 최재길대한수학회 · 대한수학회보2004 · 제41권 제1호Transforms and convolutions on function space장승준, 최재길대한수학회 · 대한수학회논문집2009 · 제24권 제3호Conditional Integral Transforms on a Function Space조동현경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제4호

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