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On the Ornstein Uhlenbeck operator perturbed by singular potentials in $L^p$--spaces
1. | Università degli Studi di Pavia, Dipartimento di Matematica “F. Casorati”, via Ferrata 1, 27100 Pavia |
2. | Dipartimento di Ingegneria dell'Informazione, Ingegneria Elletrica e Matematica Applicata, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano (Sa) |
References:
[1] |
M. Bertoldi and L. Lorenzi, "Analytical Methods for Markov Semigroups," Chapman Hall/CRC, Boca Raton FL, 2007. |
[2] |
T. Durante and A. Rhandi, On the essential self-adjointness of Ornstein-Uhlenbeck operators perturbed by inverse-square potentials, Discrete Cont. Dyn. Syst. S., 6 (2013), 649-655.
doi: doi:10.3934/dcdss.2013.6.649. |
[3] |
D. E. Edmunds and W. E. Evans, "Spectral Theory and Differential Operators," Clarendon Press, Oxford, 1987. |
[4] |
K. J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer-Verlag, New York, 2000. |
[5] |
G. R. Goldstein, J. A. Goldstein and A. Rhandi, Kolmogorov equation perturbed by an inverse-square potential, Discrete Cont. Dyn. Syst. S., 4 (2011), 623-630.
doi: 10.3934/dcdss.2011.4.623. |
[6] |
G. R. Goldstein, J. A. Goldstein and A. Rhandi, Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential, Applicable Analysis, 91 (2012), 2057-2071.
doi: 10.1080/00036811.2011.587809. |
[7] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, 1983. |
[8] |
G. Metafune, J. Prüss, A. Rhandi and R. Schnaubelt, The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), I (2002), 471-485. |
[9] |
R. Nagel, "One-Parameter Semigroups of Positive Operators," Lecture Notes in Math., 1184, Springer-Verlag, 1986. |
[10] |
N. Okazawa, On the perturbation of linear operators in Banach and Hilbert spaces, J. Math. Soc. Japan, 34 (1982), 677-701.
doi: 10.2969/jmsj/03440677. |
[11] |
N. Okazawa, $L^p$-theory of Schrödinger operators with strongly singular potentials, Japan. J. Math., 22 (1996), 199-239. |
[12] |
E. M. Ouhabaz, "Analysis of Heat Equations on Domains," London Math. Soc. Monographs, 31. Princeton Univ. Press 2004. |
[13] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness," Academic Press, New York, 1975. |
[14] |
B. Simon, Essential self-adjointness of Schrödinger operators with singular potentials, Arch. Rational Mech. Anal., 52 (1973), 44-48. |
[15] |
J. Walter, Note on a paper by Stetkœr-Hansen concerning essential self-adjointness of Schrödinger operators, Math. Scand., 25 (1969), 94-96. |
show all references
References:
[1] |
M. Bertoldi and L. Lorenzi, "Analytical Methods for Markov Semigroups," Chapman Hall/CRC, Boca Raton FL, 2007. |
[2] |
T. Durante and A. Rhandi, On the essential self-adjointness of Ornstein-Uhlenbeck operators perturbed by inverse-square potentials, Discrete Cont. Dyn. Syst. S., 6 (2013), 649-655.
doi: doi:10.3934/dcdss.2013.6.649. |
[3] |
D. E. Edmunds and W. E. Evans, "Spectral Theory and Differential Operators," Clarendon Press, Oxford, 1987. |
[4] |
K. J. Engel and R. Nagel, "One-Parameter Semigroups for Linear Evolution Equations," Springer-Verlag, New York, 2000. |
[5] |
G. R. Goldstein, J. A. Goldstein and A. Rhandi, Kolmogorov equation perturbed by an inverse-square potential, Discrete Cont. Dyn. Syst. S., 4 (2011), 623-630.
doi: 10.3934/dcdss.2011.4.623. |
[6] |
G. R. Goldstein, J. A. Goldstein and A. Rhandi, Weighted Hardy's inequality and the Kolmogorov equation perturbed by an inverse-square potential, Applicable Analysis, 91 (2012), 2057-2071.
doi: 10.1080/00036811.2011.587809. |
[7] |
D. Gilbarg and N. Trudinger, "Elliptic Partial Differential Equations of Second Order," Springer-Verlag, 1983. |
[8] |
G. Metafune, J. Prüss, A. Rhandi and R. Schnaubelt, The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), I (2002), 471-485. |
[9] |
R. Nagel, "One-Parameter Semigroups of Positive Operators," Lecture Notes in Math., 1184, Springer-Verlag, 1986. |
[10] |
N. Okazawa, On the perturbation of linear operators in Banach and Hilbert spaces, J. Math. Soc. Japan, 34 (1982), 677-701.
doi: 10.2969/jmsj/03440677. |
[11] |
N. Okazawa, $L^p$-theory of Schrödinger operators with strongly singular potentials, Japan. J. Math., 22 (1996), 199-239. |
[12] |
E. M. Ouhabaz, "Analysis of Heat Equations on Domains," London Math. Soc. Monographs, 31. Princeton Univ. Press 2004. |
[13] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness," Academic Press, New York, 1975. |
[14] |
B. Simon, Essential self-adjointness of Schrödinger operators with singular potentials, Arch. Rational Mech. Anal., 52 (1973), 44-48. |
[15] |
J. Walter, Note on a paper by Stetkœr-Hansen concerning essential self-adjointness of Schrödinger operators, Math. Scand., 25 (1969), 94-96. |
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