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Conditional generalized Fourier-Feynman transform and conditional convolution product on a Banach algebra

최재길|장승준
대한수학회 (The Korean Mathematical Society)|2004.02|대한수학회보 (Bulletin of the KMS)|제41권 제1호|pp. 73-93

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Abstract

In [10], Chang and Skoug used a generalized Brownianmotion process to define a generalized analytic Feynman integraland a generalized analytic Fourier-Feynman transform. In thispaper we define the conditional generalized Fourier-Feynmantransform and conditional generalized convolution product onfunction space. We then establish some relationships between theconditional generalized Fourier-Feynman transform and conditionalgeneralized convolution product for functionals on function spacethat belonging to a Banach algebra.

참고문헌 (15)

  1. "Brue \book A Functional Transform for Feynman Integrals Similar to the Fourier Transform \bookinfo thesis \publ University of Minnesota", pp.1~
  2. "Storvick \paper An $L_2$ analytic Fourier-Feynman transform \jour Michigan Math", pp.2~
  3. "3 \bysame \paper Some Banach algebras of analytic Feynman integrable functionals 1979 \jour Lecture Notes in Math"
  4. "Chang \paper Evaluation of some conditional Wiener integrals \jour Bull", pp.4~
  5. "Yoo \paper Analytic Fourier-Feynman transform and first variation on abstract Wienerspace", 38, pp.485~501 (2001)
  6. "paper Conditional function space integrals with applications", 26, pp.37~62
  7. "paper Integration by parts formulas involving generalized Fourier-Feynman transforms on function space", 355, pp.2925--~2948 (2003)
  8. "paper Parts formulas involving conditional Feynman integrals", 65, pp.353~369 (2002)
  9. "paper Generalized Fourier-Feynman transforms and a first variation on function space", 14, pp.375~393 (2003)
  10. "Kang \paper Conditional Wiener integrals and an integral equation \jour J", pp.12~
  11. "paper Analytic Fourier-Feynman transforms and convolution \jour Trans.", 347, pp.661~673 (1995)
  12. "paper Convolution and Fourier-Feynman transforms \jour Rocky Mountain", 27, pp.827~841 (1997)
  13. "paper Convolutions and Fourier-Feynman transforms of functionals involving multiple integrals", 43, pp.247~261 (1996)
  14. "book The Feynman Integral and Feynman's Operational Calculus", pp.18~ (2000), publ Oxford Mathematical Monographs, Clarendon Press
  15. "Skoug \paper An $L_p$ analytic Fourier-Feynman transform \jour Michigan Math", pp.19~

관련 논문AI추천

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