Heat kernel bounds, Poincaré series, and L spectrum for locally symmetric spaces
نویسنده
چکیده
We derive upper Gaussian bounds for the heat kernel on complete, non-compact locally symmetric spaces M = Γ\X with non-positive curvature. Our bounds contain the Poincaré series of the discrete group Γ and therefore we also provide upper bounds for this series.
منابع مشابه
Pointwise bounds for L eigenfunctions on locally symmetric spaces
We prove pointwise bounds for L eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with Q-rank one if the corresponding eigenvalues lie below the continuous part of the L spectrum. Furthermore, we use these bounds in order to obtain some results concerning the L spectrum.
متن کاملL spectral theory and heat dynamics of locally symmetric spaces
In this paper we first derive several results concerning the L spectrum of arithmetic locally symmetric spaces whose Q-rank equals one. In particular, we show that there is an open subset of C consisting of eigenvalues of the L Laplacian if p < 2 and that corresponding eigenfunctions are given by certain Eisenstein series. On the other hand, if p > 2 there is at most a discrete set of real eige...
متن کاملStability of heat kernel estimates for symmetric jump processes on metric measure spaces
In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, modifications of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particu...
متن کاملHolomorphic Torsion for Hermitian Locally Symmetric Spaces
Contents 1 Holomorphic torsion 5 2 The trace of the heat kernel 8 2.
متن کاملL-Spectral theory of locally symmetric spaces with Q-rank one
We study the L-spectrum of the Laplace-Beltrami operator on certain complete locally symmetric spaces M = Γ\X with finite volume and arithmetic fundamental group Γ whose universal covering X is a symmetric space of non-compact type. We also show, how the obtained results for locally symmetric spaces can be generalized to manifolds with cusps of rank one.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007