Second quantization and the Lp-spectrum of nonsymmetric Ornstein-Uhlenbeck operators

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volumn 8, Issue 3, 2005, Pages 473-495

  Van Neerven, J M A M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Invariant measure; Lp spectrum; Nonsymmetric Ornstein Uhlenbeck operators; Reproducing kernel Hilbert spaces; Second quantization; Strong Feller property; Symmetric Fock space

Indexed keywords

EID: 25144476271     PISSN: 02190257     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219025705002074     Document Type: Article

References (30)

1. S. Albeverio, V. Bogachev and M. Röckner, On uniqueness of invariant measures for finite- and infinite-dimensional diffusions, Comm. Pure Appl. Math. 52 (1999) 325-362.
2. B. Aupetit, A Primer on Spectral Theory (Springer-Verlag, 1991).
3. V. I. Bogachev, Gaussian Measures, Mathematical Surveys and Monographs, Vol. 62 (American Mathematical Society, 1998).
4. 1, in Infinite Dimensional Stochastic Analysis, Verh. Afd. Natuurkd. 1. Reeks. K. Ned. Akad. Wet., Vol. 52 (Royal Neth. Acad. Arts Sci., Amsterdam, 2000), pp. 39-54.
5. F. Bonetto, J. L. Lebowitz and J. Lukkarinen, Fourier's law for a harmonic crystal with self-consistent stochastic reservoirs, J. Statist. Phys. 116 (2004) 783-813.
6. A. Brown and C. Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966) 162-166.
7. Z. Brzeźniak and J. M. A. M. van Neerven, Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem, Studia Math. 143 (2000) 43-74.
8. A. Chojnowska-Michalik and B. Goldys, Existence, uniqueness and invariant measures for stochastic semilinear equations on Hilbert spaces, Probab. Th. Rel. Fields 102 (1995) 331-356.
9. A. Chojnowska-Michalik and B. Goldys, Nonsymmetric Ornstein-Uhlenbeck semigroup as second quantized operator, J. Math. Kyoto Univ. 36 (1996) 481-498.
10. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Encyclopedia of Mathematics and its Applications (Cambridge Univ. Press, 1992).
11. G. Da Prato and J. Zabczyk, Ergodicity for Infinite-Dimensional Systems, London Math. Soc. Lect. Note Series, Vol. 229 (Cambridge Univ. Press, 1996).
12. G. Da Prato and J. Zabczyk, Second Order Partial Differential Equations in Hilbert Spaces, London Math. Soc. Lect. Note Series, Vol. 293 (Cambridge Univ. Press, 2002).
13. p spectral independence for certain uniformly elliptic operators, in Partial Differential Equations and Mathematical Physics (Copenhagen, 1995; Lund, 1995), Progr. Nonlinear Differential Equations Appl., Vol. 21 (Birkhäuser, 1996), pp. 122-125.
14. J.-P. Eckmann and M. Hairer, Spectral properties of hypoelliptic operators, Comm. Math. Phys. 235 (2003) 233-253.
15. K.-J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194 (Springer-Verlag, 2000).
16. B. Goldys and M. Musiela, Infinite dimensional diffusions, Kolmogorov equations and interest rate models. Option pricing, interest rates and risk management, in Handbook of Mathematical Finance (Cambridge Univ. Press, 2001), pp. 314-335.
17. B. Goldys and J. M. A. M. van Neerven, Transition semigroups of Banach space valued Ornstein-Uhlenbeck processes, Acta Appl. Math. 76 (2003) 283-330.
18. R. Gunning and B. Rossi, Analytic Functions of Several Complex Variables (Prentice-Hall, 1965).
19. ν) is p-independent, Comm. Math. Phys. 104 (1986) 243-250.
20. 2, J. Oper. Th. 7 (1982) 61-78.
21. S. Janson, Gaussian Hilbert Spaces, Cambridge Tracts in Mathematics, Vol. 129 (Cambridge Univ. Press, 1997).
22. p-spectrum of Ornstein-Uhlenbeck operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 30 (2001) 97-124.
23. n, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 11 (2000) 9-19.
24. p spaces with respect to invariant measures, J. Funct. Anal. 196 (2002) 40-60.
25. G. Metafune, A. Rhandi and R. Schnaubelt, Spectrum of the infinite-dimensional Laplacian, Arch. Math. (Basel) 75 (2000) 280-282.
26. J. M. A. M. van Neerven, Nonsymmetric Ornstein-Uhlenbeck semigroups in Banach spaces, J. Funct. Anal. 155 (1998) 495-535.
27. K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Monographs in Mathematics, Vol. 85 (Birkhäuser, 1992).
28. M. Reed and B. Simon, Tensor products of closed operators on Banach spaces, J. Funct. Anal. 13 (1973) 107-124.
29. M. Schechter, On the spectra of operators on tensor products, J. Funct. Anal. 4 (1969) 95-99.
30. 2 Euclidean (Quantum) Field Theory, Princeton Series in Physics (Princeton Univ. Press, 1974).