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Schauder estimates for some perturbation of an infinite dimensional Ornstein--Uhlenbeck operator
On the essential self-adjointness of Ornstein-Uhlenbeck operators perturbed by inverse-square potentials
1. | Dipartimento di Ingegneria dell'Informazione, Ingegneria Elletrica e Matematica Applicata, Università degli Studi di Salerno, Via Ponte Don Melillo, 84084 Fisciano (Sa), Italy, Italy |
References:
[1] |
P. Baras and J. A. Goldstein, The heat equation with singular potential, Trans. Amer. Math. Soc., 284 (1984), 121-139.
doi: 10.2307/1999277. |
[2] |
M. Bertoldi and L. Lorenzi, "Analytical Methods for Markov Semigroups," Pure and Applied Mathematics, 283, CRC Press, 2006. |
[3] |
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.
doi: 10.1080/00036811.2011.587809. |
[4] |
T. Ikebe and T. Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal., 9 (1962), 77-92. |
[5] |
H. Kalf, U. W. Schmincke, J. Walter and R. Wüst, "On the Spectral Theory of Schrödinger and Dirac Operators with Strongly Singular Potentials," Spectral Theory and Differential Equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., 449, 182-226. Springer, Berlin, 1975. |
[6] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness," Academic Press, New York, 1975. |
[7] |
B. Simon, Essential self-adjointness of Schrödinger operators with singular potentials, Arch. Rational Mech. Anal., 52 (1973), 44-48. |
[8] |
J. Walter, Note on a paper by Stetkær-Hansen concerning essential self-adjointness of Schrödinger operators, Math. Scand., 25 (1969), 94-96. |
show all references
References:
[1] |
P. Baras and J. A. Goldstein, The heat equation with singular potential, Trans. Amer. Math. Soc., 284 (1984), 121-139.
doi: 10.2307/1999277. |
[2] |
M. Bertoldi and L. Lorenzi, "Analytical Methods for Markov Semigroups," Pure and Applied Mathematics, 283, CRC Press, 2006. |
[3] |
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.
doi: 10.1080/00036811.2011.587809. |
[4] |
T. Ikebe and T. Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal., 9 (1962), 77-92. |
[5] |
H. Kalf, U. W. Schmincke, J. Walter and R. Wüst, "On the Spectral Theory of Schrödinger and Dirac Operators with Strongly Singular Potentials," Spectral Theory and Differential Equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., 449, 182-226. Springer, Berlin, 1975. |
[6] |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics II: Fourier Analysis, Self-Adjointness," Academic Press, New York, 1975. |
[7] |
B. Simon, Essential self-adjointness of Schrödinger operators with singular potentials, Arch. Rational Mech. Anal., 52 (1973), 44-48. |
[8] |
J. Walter, Note on a paper by Stetkær-Hansen concerning essential self-adjointness of Schrödinger operators, Math. Scand., 25 (1969), 94-96. |
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