Hypercontractivity for perturbed diffusion semigroups
Annales de la Faculté des sciences de Toulouse : Mathématiques (2005)
- Volume: 14, Issue: 4, page 609-628
- ISSN: 0240-2963
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topCattiaux, Patrick. "Hypercontractivity for perturbed diffusion semigroups." Annales de la Faculté des sciences de Toulouse : Mathématiques 14.4 (2005): 609-628. <http://eudml.org/doc/73660>.
@article{Cattiaux2005,
author = {Cattiaux, Patrick},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {Log-Sobolev inequality; Boltzmann measure},
language = {eng},
number = {4},
pages = {609-628},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Hypercontractivity for perturbed diffusion semigroups},
url = {http://eudml.org/doc/73660},
volume = {14},
year = {2005},
}
TY - JOUR
AU - Cattiaux, Patrick
TI - Hypercontractivity for perturbed diffusion semigroups
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2005
PB - Université Paul Sabatier, Institut de Mathématiques
VL - 14
IS - 4
SP - 609
EP - 628
LA - eng
KW - Log-Sobolev inequality; Boltzmann measure
UR - http://eudml.org/doc/73660
ER -
References
top- [1] Aida ( S.). — An estimate of the gap of spectrum of Schrödinger operators which generate hyperbounded semigroups, J. Func. Anal.185, p. 474-526 (2001). Zbl1038.60077
- [2] Aida ( S.) , Shigekawa ( I.). — Logarithmic Sobolev inequalities and spectral gaps: perturbation theory, J. Func. Anal.126, p. 448-475 (1994). Zbl0846.46019MR1305076
- [3] Ané ( C. ) , Blachère ( S.), Chafai ( D.), Fougères ( P.), Gentil ( I.), Malrieu ( F.), Roberto ( C.), Scheffer ( G.).— Sur les inégalités de Sobolev logarithmiques, volume 10 of Panoramas et Synthèses. S.M.F, Paris (2000). Zbl0982.46026
- [4] Bakry ( D.). — L'hypercontractivité et son utilisation en théorie des semi groupes, Ecole d'été de Probabilités de Saint-Flour. Lect. Notes Math1581, p. 1-114 (1994). Zbl0856.47026MR1307413
- [5] Barthe ( F. ), Cattiaux ( P.), Roberto ( C.). — Interpolated inequalities between exponential and gaussian, Orlicz hypercontractivity and application to isoperimetry, Preprint (2004).
- [6] Cattiaux ( P.). — A pathwise approach of some classical inequalities, Potential Analysis20, p. 361-394 (2004). Zbl1050.47041MR2032116
- [7] Cattiaux ( P.), Léonard ( C.) . - Minimization of the Kullback information for general Markov processes. Séminaire de ProbasXXX, Lect. Notes Math1626, p. 283-311 (1996). Zbl0863.60073
- [8] Davies ( E.B. ). — Heat kernels and spectral theory , Cambridge University Press (1989 ). Zbl0699.35006MR990239
- [9] Deuschel ( J.D. ), Stroock ( D.W.). — Large deviations, Academic Press (1989). Zbl0705.60029MR997938
- [10] Gong ( F.Z. ), Wu ( L.M.).— Spectral gap of positive operators and its applications, C. R. Acad. Sci. Paris, Sér. 1, t 331, p. 983-988 (2000). Zbl0984.47030MR1809440
- [11] Gross ( L.). — Logarithmic Sobolev inequalities and contractivity properties of semi-groups, in Dirichlet forms, Dell'Antonio and Mosco eds, Lect. Notes Math1563, p. 54-88 (1993). Zbl0812.47037MR1292277
- [12] Guionnet ( A.), Zegarlinski ( B.).— Lectures on logarithmic Sobolev inequalities, Séminaire de ProbabilitésXXXVI, Lect. Notes Math1801, (2002). MR1971582
- [13] Kavian ( O. ), Kerkyacharian ( G.), Roynette ( B.).— Quelques remarques sur l'ultracontractivité, J. Func. Anal.111, p. 155-196 (1993). Zbl0807.47027MR1200640
- [14] Kunz ( A.). — On extremes of multidimensional stationary diffusion processes in euclidean norm, Preprint (2002).
- [15] Kusuoka ( S.), Stroock ( D.). — Some boundedness properties of certain stationary diffusion semigroups, J. Func. Anal.60, p. 243-264 (1985). Zbl0562.60078MR777238
- [16] Ledoux ( M. ). — Concentration of measure and logarithmic Sobolev inequalities, Séminaire de ProbasXXXIII, Lect. Notes Math1709, p. 120-216 (1999). Zbl0957.60016MR1767995
- [17] Mathieu ( P.). — Quand l'inégalité Log-Sobolev implique l'inégalité de trou spectral, Séminaire de ProbasXXXII, Lect. Notes Math1686, p. 30-35 (1998).
- [18] Röckner ( M.), Wang ( F.Y.). — Weak Poincaré inequalities and L2 convergence rates of Markov semigroups, J. Func. Anal.185 , p. 564-603 (2001). Zbl1009.47028
- [19] Rosen ( J. ).— Sobolev inequalities for weight spaces and supercontractivity, Trans. Amer. Math. Soc.222, p. 367-376 (1976). Zbl0344.46072MR425601
- [20] Royer ( G.). — Une initiation aux inégalités de Sobolev logarithmiques , S.M.F., Paris ( 1999). Zbl0927.60006
- [21] Wang ( F.Y. ).— Logarithmic Sobolev inequalities: conditions and counterexamples, J. Operator Theory46, p. 183-197 (2001). Zbl0993.58019MR1862186
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