• Chang, Seung Jun (Department of Mathematics Dankook University) ;
  • Choi, Jae Gil (Department of Mathematics Dankook University) ;
  • Skoug, David (Department of Mathematics University of Nebraska-Lincoln)
  • Received : 2014.04.14
  • Published : 2015.01.01


The purpose of this paper is first of all to investigate the behavior of admixable operators on the product of abstract Wiener spaces and secondly to examine transform semigroups which consist of admix-Wiener transforms on abstract Wiener spaces.


abstract Wiener space;admixable operator;admix-Wiener transform;transform semigroup


  1. R. H. Cameron and D. A. Storvick, An operator valued Yeh-Wiener integral, and a Wiener integral equation, Indiana Univ. Math. J. 25 (1976), no. 3, 235-258.
  2. J. E. Bearman, Rotations in the product of two Wiener spaces, Proc. Amer. Math. Soc. 3 (1952), no. 1, 129-137.
  3. J. G. Choi and S. J. Chang, A rotation of admixable operators on abstract Wiener space with applications, J. Funct. Space Appl. 2013 (2013), Article ID 671909, 12 pages.
  4. D. M. Chung, Scale-invariant measurability in abstract Wiener spaces, Pacific J. Math. 130 (1987), no. 1, 27-40.
  5. D. M. Chung, C. Park, and D. Skoug, Generalized Feynman integrals via conditional Feynman integrals, Michigan Math. J. 40 (1993), no. 2, 377-391.
  6. D. L. Cohn, Measure Theory, Second edition, Birkhauser Advanced Texts Basler Lehrbucher, Birkhauser, Boston, 2013.
  7. L. Gross, Abstract Wiener spaces, Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, vol. 2, pp. 31-42, University of California Press, Berkeley, 1965.
  8. T. Huffman, C. Park, and D. Skoug, Generalized transforms and convolutions, Int. J. Math. Math. Sci. 20 (1997), no. 1, 19-32.
  9. G. W. Johnson and D. L. Skoug, The Cameron-Storvick function space integral: An L($L_p$, $L_{p{\prime}}$) theory, Nagoya Math. J. 60 (1976), 93-137.
  10. H.-H. Kuo, Gaussian Measures in Banach Spaces, Lecture Notes in Math. 463, Springer, Berlin, 1975.
  11. G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math. 83 (1979), no. 1, 157-176.
  12. G. W. Johnson and D. L. Skoug, Notes on the Feynman integral. II, J. Funct. Anal. 41 (1981), no. 3, 277-289.
  13. G. Kallianpur and C. Bromley, Generalized Feynman integrals using analytic continu-ation in several complex variables, Stochastic Analysis and Applications, pp. 217-267, Dekker, New York, 1984.
  14. Y.-J. Lee, Integral transforms of analytic functions on abstract Wiener spaces, J. Funct. Anal. 47 (1982), no. 2, 153-164.
  15. R. E. A. C. Paley, N. Wiener, and A. Zygmund, Notes on random functions, Math. Z. 37 (1933), no. 1, 647-668.
  16. C. Park and D. Skoug, A note on Paley-Wiener-Zygmund stochastic integrals, Proc. Amer. Math. Soc. 103 (1988), no. 2, 591-601.
  17. C. Park and D. Skoug, A Kac-Feynman integral equation for conditional Wiener integrals, J. Integral Equations Appl. 3 (1991), no. 3, 411-427.
  18. C. Park and D. Skoug, Generalized Feynman integrals: The L($L_2$, $L_2$) theory, Rocky Mountain J. Math. 25 (1995), no. 2, 739-756.
  19. C. Park and D. Skoug, Conditional Fourier-Feynman transforms and conditional convolution products, J. Korean Math. Soc. 38 (2001), no. 1, 61-76.