L p -spectrum of Ornstein-Uhlenbeck operators
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 1, p. 97-124
@article{ASNSP_2001_4_30_1_97_0,
     author = {Metafune, Giorgio},
     title = {$L^p$-spectrum of Ornstein-Uhlenbeck operators},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 30},
     number = {1},
     year = {2001},
     pages = {97-124},
     zbl = {1065.35216},
     mrnumber = {1882026},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2001_4_30_1_97_0}
}
Metafune, Giorgio. $L^p$-spectrum of Ornstein-Uhlenbeck operators. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 30 (2001) no. 1, pp. 97-124. http://www.numdam.org/item/ASNSP_2001_4_30_1_97_0/

[1] W. Arendt, Gaussian estimates and interpolation of the spectrum in LP, Differential Integral Equations 7 (1994), 1153-1168. | MR 1269649 | Zbl 0827.35081

[2] W. Arendt - F. Räbiger - A. Sourour, Spectral properties of the operator equation A X + X B = Y, Quart. J. Math. Oxford Ser. (2) 45 (1994), 133-149. | MR 1280689 | Zbl 0826.47013

[3] D. Bakry, L'hypercontractivite et son utilisation en theorie des semi-groupes, in: D. Bakry, R. D. Gill, S. A. Molchanov, Lectures on probability theory, Springer LNM 1581, (1992), 1-114. | MR 1307413 | Zbl 0856.47026

[4] D.W. Boyd, The spectrum of the Cesaro operator, Acta Sci. Math. 29 (1968), 31-34. | MR 239441 | Zbl 0157.45501

[5] S. Cerrai, Elliptic and parabolic equations in Rn with coefficients having polynomial growth, Comm. Partial Differential Equations 21 (1996), 281-317. | MR 1373775 | Zbl 0851.35049

[6] G. Da Prato - A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal. 131 (1995), 94-114. | MR 1343161 | Zbl 0846.47004

[7] G. Da Prato - J. Zabczyk, "Ergodicity for Infinite Dimensional Systems", Univ. Press, Cambridge, 1996. | MR 1417491 | Zbl 0849.60052

[8] E.B. Davies - B. Simon, L1 properties of intrinsic Schrödinger semigroups, J. Funct. Anal. 65 (1986), 126-146. | MR 819177 | Zbl 0613.47039

[9] B. Goldys, On Analyticity of Ornstein- Uhlenbeck semigroups, Rend. Mat. Acc. Lincei (9) 10 (1999), 131-140. | MR 1769162 | Zbl 1026.47506

[10] L. Hörmander, Hypoelliptic differential operators of second order, Acta Math. 119 (1967), 147-171. | MR 222474 | Zbl 0156.10701

[11] K. Engel - R. Nagel, "One-parameters Semigroup for Linear Evolution Equations", 194 Springer Graduate Texts in Mathematics, 2000. | MR 1721989 | Zbl 0952.47036

[12] A. Erdelyi, "Asymptotic Expansions", Dover, 1956. | MR 78494 | Zbl 0070.29002

[13] A. Lunardi, Schauder estimates for a class of degenerate elliptic and parabolic operators with unbounded coefficients in Rn, Ann. Scuola Norm. Sup. Pisa Cl. Sc. (4) 24 (1997), 133-164. | Numdam | MR 1475774 | Zbl 0887.35062

[14] A. Lunardi, On the Ornstein-Uhlenbeck operator in L 2 spaces with respect to invariant measures, Trans. Amer. Math. Soc. 349 (1997), 155-169. | MR 1389786 | Zbl 0890.35030

[15] A. Lunardi - V. Vespri, Generation of smoothing semigroups by elliptic operators with unbounded coefficients in Rn,, Rend. Istit. Mat. Univ. Trieste 28 (1997), 251-279. | MR 1602271 | Zbl 0899.35027

[16] A. Lunardi - V. Vespri, Optimal L∞ and Schauder estimates for elliptic and parabolic operators with unbounded coefficients, In: Proc. Conf. "Reaction-diffusion systems" G. Caristi - E. Mitidieri (eds.), Lecture notes in pure and applied mathematics 194, M. Dekker (1998), 217-239. | Zbl 0887.47034

[17] P.A. Meyer, Note sur ler processus d'Ornstein-Uhlenbeck, Seminaire de probabilités XVI, Springer LNM 920 (1982), 95-133. | Numdam | MR 658673 | Zbl 0481.60041

[18] J.M.A.M. Van Neerven - J. Zabczyk, Norm discontinuity of Ornstein-Uhlenbeck semigroups, Semigroup Forum 59 (1999), 389-403. | MR 1847653 | Zbl 0960.47024

[19] E.M. Stein - G. Weiss, "Introduction to Fourier Analysis on Euclidean Spaces", Princeton Univ. Press, 1971. | MR 304972 | Zbl 0232.42007

[20] E.T. Whittaker - G.N. Watson, "A course of Modem Analysis", Cambridge Univ. Press, Cambridge, 1927. | JFM 53.0180.04

[21] L. Weis, The stability of positive semigroups on L p spaces, Proc. Amer. Math. Soc. 123 (1995), 3089-3094. | MR 1273529 | Zbl 0851.47028