A Cameron-Storvick Theorem for Analytic Feynman Integrals on Product Abstract Wiener Space and Applications

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• 作者：Jae Gil Choi (1)
  Seung Jun Chang (1)
  
• 关键词：Cameron鈥揝torvick theorem ; Abstract Wiener space ; Analytic Feynman integral ; First variation ; Generalized Fresnel class
• 刊名：Applied Mathematics and Optimization
• 出版年：2013
• 出版时间：April 2013
• 年：2013
• 卷：67
• 期：2
• 页码：243-260
• 全文大小：651KB
• 参考文献：1. Albeverio, S., H酶egh-Krohn, R.: Mathematical Theory of Feynman Path Integrals. Lecture Notes in Math., vol. 523. Springer, Berlin (1976)
  2. Cameron, R.H.: The first variation of an indefinite Wiener integral. Proc. Am. Math. Soc. 2, 914鈥?24 (1951) CrossRef
  3. Cameron, R.H., Storvick, D.A.: Feynman integral of variations of functionals. In: It么, K., Hida, T. (eds.) Gaussian Random Fields. Ser. Probab. Stat., pp. 144鈥?57. World Scientific, Singapore (1991)
  4. Chang, K.S., Kim, B.S., Yoo, I.: Analytic Fourier-Feynman transform and convolution of functionals on abstract Wiener space. Rocky Mt. J. Math. 30, 823鈥?42 (2000) CrossRef
  5. Chang, S.J., Choi, J.G., Skoug, D.: Evaluation formulas for conditional function space integrals I. Stoch. Anal. Appl. 25, 141鈥?68 (2007) CrossRef
  6. Chang, S.J., Choi, J.G., Skoug, D.: A generalized analytic Fourier-Feynman transform on the product function space $C_{a,b}^{2}[0,T]$ and related topics. (Submitted for publication)
  7. Chung, H.S., Chang, S.J., Choi, J.G.: A sequential approach for function space transforms. (Submitted for publication)
  8. Chung, D.M.: Scale-invariant measurability in abstract Wiener spaces. Pac. J. Math. 130, 27鈥?0 (1987) CrossRef
  9. Folland, G.B.: Real Analysis, 2nd edn. Wiley, New York (1999)
  10. Gross, L.: Abstract Wiener spaces. In: Proc. Fifth, Berkeley Sym. Math. Stat. Probab.. vol.聽2, pp.聽31鈥?2 (1965)
  11. Johnson, G.W., Lapidus, M.L.: the Feynman Integral and Feynman鈥檚 Operational Calculus. Clarendon Press, Oxford (2000)
  12. Kallianpur, G., Bromley, C.: Generalized Feynman integrals using analytic continuation in several complex variables. In: Pinsky, M. (ed.) Stochastic Analysis and Applications, pp. 217鈥?67. Dekker, New York (1984)
  13. Kallianpur, G., Kannan, D., Karandikar, R.L.: Analytic and sequential Feynman integrals on abstract Wiener and Hilbert spaces and a Cameron-Martin formula. Ann. Inst. Henri Poincar茅 21, 323鈥?61 (1985)
  14. Kuelbs, J.: Abstract Wiener spaces and applications to analysis. Pac. J. Math. 31, 433鈥?50 (1969) CrossRef
  15. Kuo, H.-H.: Gaussian Measures in Banach Spaces. Lecture Notes in Math., vol. 463. Springer, Berlin (1975)
  16. Yoo, I.: Notes on a generalized Fresnel class. Appl. Math. Optim. 30, 225鈥?33 (1994) CrossRef
  
• 作者单位：Jae Gil Choi (1)
  Seung Jun Chang (1)
  
  1. Department of Mathematics, Dankook University, Cheonan, 330-714, Korea
  
• ISSN：1432-0606

文摘

In this paper we derive a Cameron-Storvick theorem for the analytic Feynman integral of functionals on product abstract Wiener space B 2. We then apply our result to obtain an evaluation formula for the analytic Feynman integral of unbounded functionals on B 2. We also present meaningful examples involving functionals which arise naturally in quantum mechanics.