Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap
Tài liệu tham khảo
Auscher, 2004, Riesz transform on manifolds and heat kernel regularity, Ann. Sci. École Norm. Sup. (4), 37, 911, 10.1016/j.ansens.2004.10.003
Bakry, 1985, Transformations de Riesz pour les semi-groupes symétriques, vol. 1123, 130
Bakry, 1989, The Riesz transforms associated with second order differential operators, vol. 17, 1
Borel, 1983, Laplacian and the discrete spectrum of an arithmetic group, Amer. J. Math., 105, 309, 10.2307/2374262
Brooks, 1981, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv., 56, 581, 10.1007/BF02566228
Buser, 1982, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. (4), 15, 213, 10.24033/asens.1426
Coulhon, 1999, Riesz transforms for 1⩽p⩽2, Trans. Amer. Math. Soc., 351, 1151, 10.1090/S0002-9947-99-02090-5
Donnelly, 1979, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J., 46, 497, 10.1215/S0012-7094-79-04624-6
Doyle, 1988, On the bass note of a Schottky group, Acta Math., 160, 249, 10.1007/BF02392277
Ji, 2008, Pointwise bounds for L2 eigenfunctions on locally symmetric spaces, Ann. Global Anal. Geom., 34, 387, 10.1007/s10455-008-9116-x
Lax, 1982, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Funct. Anal., 46, 280, 10.1016/0022-1236(82)90050-7
Leuzinger, 2004, Critical exponents of discrete groups and L2-spectrum, Proc. Amer. Math. Soc., 132, 919, 10.1090/S0002-9939-03-07173-9
Mandouvalos, 2009, Spectrum of the Laplacian and Riesz transform on locally symmetric spaces, Bull. Sci. Math., 133, 134, 10.1016/j.bulsci.2008.04.005
Müller, 1987, Manifolds with Cusps of Rank One, Spectral Theory and L2-Index Theorem, vol. 1244
Strichartz, 1983, Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52, 48, 10.1016/0022-1236(83)90090-3
Sturm, 1993, On the Lp-spectrum of uniformly elliptic operators on Riemannian manifolds, J. Funct. Anal., 118, 442, 10.1006/jfan.1993.1150
Taylor, 1989, Lp-estimates on functions of the Laplace operator, Duke Math. J., 58, 773, 10.1215/S0012-7094-89-05836-5
2008
Thurston
Triebel, 1995
Weber, 2008, Heat kernel bounds, Poincaré series, and L2 spectrum for locally symmetric spaces, Bull. Austral. Math. Soc., 78, 73, 10.1017/S0004972708000488