An extension of the bolsinov-fomenko theorem on orbital classification of integrable hamiltonian systems

Rocky Mountain Journal of Mathematics

Volumn 30, Issue 2, 2000, Pages 477-496

  Chang, Seung Jun ^a   Park, Chull ^b   Skoug, David ^c  

^a Dankook University   (South Korea)

^b MIAMI UNIVERSITY   (United States)

^c UNIVERSITY OF NEBRASKA LINCOLN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034347763     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1022009276     Document Type: Article

References (29)

1. M.D. Brue, A functional transform for Feynman integrals similar to the Fourier transform, Ph.D. Thesis, University of Minnesota, Minneapolis, 1972.
2. R.H. Cameron and G.E. Graves, Additional functionals on a space of continuous functions, I, Trans. Amer. Math. Soc. 70 (1951), 160-176.
3. R.H. Cameron and W.T. Martin, Transformations of Wiener integrals under translations, Ann. of Math. 45 (1944), 386-396.
4. R.H. Cameron and D.A. Storvick, A translation theorem for analytic Feynman integrals, Trans. Amer. Math. Soc. 125 (1966), 1-6.
5. R.H. Cameron and D.A. Storvick, An L2 analytic Fourier-Feynman transform, Michigan Math. J. 23 (1976), 1-30.
6. R.H. Cameron and D.A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, Analytic functions (Kozubnik, 1979), Lecture Notes in Math. 798, Springer, Berlin, 1980, 18-67.
7. R.H. Cameron and D.A. Storvick, A new translation theorem for the analytic Feynman integral, Rev. Roum. Math. Pures Appl. 27 (1982), 937-944.
8. R.H. Cameron and D.A. Storvick, A simple definition of the Feynman integral, with applications, Mem. Amer. Math. Soc. 46 (1983), 1-46.
9. K.S. Chang, Scale-invariant measurability in Yeh-Wiener Space, J. Korean Math. Soc. 19 (1982), 61-67.
10. K.S. Chang, G.W. Johnson and D.L. Skoug, Functions in the Banach algebra S(v), J. Korean Math. Soc. 24 (1987), 151-158.
11. S.J. Chang and D.M. Chung, A class of conditional Wiener integrals, J. Korean Math. Soc. 30 (1993), 161-172.
12. D.M. Chung and S.J. Kang, Translation theorems for Feynman integrals on abstract Wiener and Hilbert spaces, Bull. Korean Math. Soc. 23 (1986), 177-187.
13. D.M. Chung, C. Park and D.L. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J. 40 (1993), 377-391.
14. D.M. Chung and D.L. Skoug, Conditional analytic Feynman integrals and a related Schrodinger integral equation, SIAM J. Math. Anal. 20 (1989), 950-965.
15. T. Huffman, C. Park and D. Skoug, Analytic Fourier-Feynman transforms and convolution, Trans. Amer. Math. Soc. 347 (1995), 661-673.
16. T. Huffman, C. Park and D. Skoug, Convolution and Fourier-Feynman transforms, Rocky Mountain J. Math. 27 (1997), 827-841.
17. T. Huffman, C. Park and D. Skoug, Convolutions and Fourier-Feynman transforms of functionals in volving multiple integrals, Michigan Math. J. 43 (1996), 247-261.
18. T. Huffman, C. Park and D. Skoug, Generalized transforms and convolutions, Internat. J. Math. Math. Sci. 20 (1997), 19-32.
19. pr) theory, Nagoya Math. J. 60 (1976), 93-137.
20. G.W. Johnson and D.L. Skoug, An Lp analytic Fourier-Feynman transform, Michigan Math. J. 26 (1979), 103-127.
21. G.W. Johnson and D.L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math 83 (1979), 157-176.
22. G.W. Johnson and D.L. Skoug, Notes on the Feynman integral, III, Pacific J. Math. 105 (1983), 321-358.
23. C. Park and D. Skoug, A simple formula for conditional Wiener integrals with applications, Pacific J. Math. 135 (1988), 381-394.
24. C. Park and D. Skoug, A Kac-Feynman integral equation for conditional Wiener integrals, J. Integral Equations Appl. 3 (1991), 411-427.
25. C. Park and D. Skoug, The Feynman integral of quadratic potentials depending on n time parameters, Nagoya Math. J. 110 (1998), 151-162.
26. C. Park and D. Skoug, Conditional Fourier-Feynman transformations and conditional con volution products, submitted.
27. I. Segal, Transformations in Wiener space and squares of quantum fields, Adv. Math. 4 (1970), 91-108.
28. D.A. Storvick, The analytic Feynman integral, in Dirichlet forms and stochastic processes, Proc. of the Internat. Conf., Beijing, China, 1993, 355-362.
29. J. Yeh, Inversion of conditional Wiener integrals, Pacific J. Math. 59 (1975), 623-638.