Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지

ONE-PARAMETER GROUPS AND COSINE FAMILIES OF OPERATORS ON WHITE NOISE FUNCTIONS

  • Chung, Chang-Hoon (Department of Mathematics College of Natural Science Chungbuk of Natural Science Chunguk National University) ;
  • Chung, Dong-Myung (Department of Mathematics Sogang University) ;
  • Ji, Un-Cig (Department of Mathematice Seoul National University)
  • Published : 2000.09.01
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Abstract

The main purpose of this paper is to study differentiable one-parameter groups and cosine families of operators acting on white noise functions and their associated infinitesimal generators. In particular, we prove the heredity of differentiable one-parameter group and cosine family of operators under the second quantization of the Cuchy problems for the first and second or der differential equations.

Keywords

References

  1. Nagoya Math. J. v.147 Transforms on white noise functionals with their applications to Cauchy problems D. M. Chung;U. C. Ji
  2. Appl. Math. Optim v.37 Transformation groups on white noise functionals and their applications
  3. Stoch. Anal. Appl. v.17 Some Cauchy problems in white noise analysis and associated semigroups of operators
  4. Nagoya Math. J. v.149 Transformations on white noise functions associated with second order differential operators of diagonal type D. M. Chung;U. C. Ji;N. Obata
  5. Infinite Dim. Anal. Quantum Prob. v.1 Higher powers of quantum white noises in terms of integral kernel operators
  6. Infinite Dim. Anal. Quantum Prob. v.2 Cauchy problems associated with Levy Laplacian in white noise analysis D. M. Chung;U. C. Ji;K. Saito
  7. Infinite Dim. Anal. Quantum Prob. v.1 A new class of white noise generalized functions W. G. Cochran;H.-H. Kuo;A. Sengupta
  8. in Pitman Research Notes in Math. Ser. v.310 Fourier transform and heat equation in white noise analysis I. Doku;H.-H. Kuo;Y. J. Lee
  9. J. Combin. Theory Ser. v.A 65 On the average rank of an element in a Filter of the partition lattice K. Engel
  10. J. Funct. Anal. v.1 Potential theory on Hilbert space L. Gross
  11. Carleton Math. Lect. Notes v.13 Analysis of brounian functionals T. Hida
  12. Nagoya Math. J. v.128 Infinite dimensional rotations and Laplacians in terms of white noise calculus T. Hida;N. Obata;K. Saito K
  13. J. Funct. Anal. v.11 Transformations for white noise functionals T. Hida;H.-H. Kuo;N. Obata
  14. White noise: An Infinite Dimensional Calculus T. Hida;H.-H. Kuo;J. Potthoff;L. Streit
  15. Soochow J. Math. v.20 Heat and Poisson equations associated with number operator in white noise analysis S. J. Kang
  16. J. Korean Math. Soc. v.33 Heat equation in white noise analysis J. S. Kim Lee
  17. Rep. Math. Phys. v.33 Spaces of white noise distributions: Constructiosn, descriptions, applications I Yu. U. Kondratiev;L. Streit
  18. Proc. Japan Acad. v.56A Calculus on Gaussian white noise I-IV I. Kubo;S. Takenaka
  19. in Lect. Notes in Math. v.1203 On Laplacian operators of generalized Brownian functionals H.-H. Kuo
  20. in Lect. Notes in Math. v.1236 The Heat equation and Fourier transforms of generalized Brownion functionals
  21. Lect. Notes in Math. v.1390 Stochastic differential equations of generalized Brownian functionals
  22. White Noise Distribution Theory
  23. Trans. Amer. Math. Soc. v.262 Applications of the Fourier-Wiener transform to differential equations on infinite dimensinal space I Y. J. Lee
  24. J. Math. Soc. Japan v.45 An analytic characterization of symbols of operators on white noise functionals N. Obata
  25. Lect. Notes in Math. v.1577 White noise calculus and Fock space
  26. Mh. Math. v.124 Constructing one-parameter transformations on white noise functions in terms of equicontinuous generators
  27. Trans. Amer. Math. Soc. v.194 Parabolic equations associated with the number operator M. A. Piech
  28. J. Funct. Anal. v.101 A characterization of Hida distributions J. Potthoff;L. Streit
  29. in Pitman Research Notes in Math. Ser. v.310 A group generated by the Levy Laplacian and the Fourier-Mehler transform K. Saito
  30. Infinite Dim. Anal. Quantum Prob. v.1 A Co-group generated by the Levy Laplacian II