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Convolutions of white noise operators

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Motivated by the convolution product of white noise functionals,we introduce a new notion of convolution products of white noise operators. Then we study several interesting relations between the convolution products and the quantum generalized Fourier-Mehler transforms,and study a quantum-classical correspondence.

Abstract

Motivated by the convolution product of white noise functionals,we introduce a new notion of convolution products of white noise operators. Then we study several interesting relations between the convolution products and the quantum generalized Fourier-Mehler transforms,and study a quantum-classical correspondence.

참고문헌 (15)

  1. M. Ben Chrouda, "Quantum stochastic processes and applications, Quantum probability and infinite dimensional analysis", QP-PQ: Quantum Probab. White Noise Anal, 18, pp.115~125 (2005), World Sci. Publ., Hackensack, NJ
  2. D. M. Chung, "Transforms on white noise functionals with their applications to Cauchy problems", Nagoya Math. J, 147, pp.1~23 (1997)
  3. D. M. Chung, "Transformation groups on white noise functionals and their applications", Appl. Math. Optim, 37(2), pp.205~223 (1998)
  4. D. M. Chung, "Quantum stochastic analysis via white noise operators in weighted Fock space", Rev. Math. Phys, 14(3), pp.241~272 (2002)
  5. T. Hida, "Analysis of Brownian Functionals", Carleton Math. Lect, 13 (1975), Carleton University
  6. R. L. Hudson, "Quantum Ito's formula and stochastic evolu- tions", Comm. Math. Phys, 93(3), pp.301~323 (1984)
  7. 지운식, "Quantum extensions of Fourier-Gauss and Fourier-Mehler transforms", 대한수학회지, 45(6), pp.1785~1801 (2008), 대한수학회
  8. U. C. Ji, "Quantum white noise calculus, In Non-Commutativity, Infinite- Dimensionality and Probability at the Crossroads", pp.143~191 (2002), World Scientific
  9. U. C. Ji, "A unified characterization theorem in white noise theory", Infin. Dimens. Anal. Quantum Probab. Relat. Top, 6(2), pp.167~178 (2003)
  10. 지운식, "Annihilation-Derivative, Creation-Derivative and Representation of Quantum Martingales", COMMUNICATIONS IN MATHEMATICAL PHYSICS, 286(2), pp.751~775
  11. H.-H. Kuo, "White Noise Distribution Theory" (1996), CRC Press
  12. P.-A. Meyer, "Quantum Probability for Probabilists", Lect. Notes in Math, 1538 (1993), Springer-Verlag
  13. N. Obata, "White Noise Calculus and Fock Space", Lect. Notes in Math, 1577 (1994), Springer-Verlag
  14. N. Obata, "An analytic characterization of symbols of operators on white noise functionals", J. Math. Soc. Japan, 45(3), pp.421~445 (1993)
  15. K. R. Parthasarathy, "An Introduction to Quantum Stochastic Calculus" (1992), Birkhauser

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