Pointwise bounds for L eigenfunctions on locally symmetric spaces
نویسندگان
چکیده
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.
منابع مشابه
Heat kernel bounds, Poincaré series, and L spectrum for locally symmetric spaces
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.
متن کاملL p norms of higher rank eigenfunctions and bounds for spherical functions
We prove almost sharp upper bounds for the Lp norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of new asymptotic bounds for spherical functions that are of inde...
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 کاملPointwise Eigenfunction Estimates and Intrinsic Ultracontractivity-type Properties of Feynman-kac Semigroups for a Class of Lévy Processes
We introduce a class of Lévy processes subject to specific regularity conditions, and consider their Feynman-Kac semigroups given under a Kato-class potential. Using new techniques, first we analyze the rate of decay of eigenfunctions at infinity. We prove bounds on λ-subaveraging functions, from which we derive two-sided sharp pointwise estimates on the ground state, and obtain upper bounds on...
متن کاملLower Bounds for Eigenvalues of Elliptic Operators: By Nonconforming Finite Element Methods
The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation properties of nonconforming finite element spaces Vh are better than global continuity properties of Vh, corresponding methods will produce lower bounds for eigenvalu...
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 2008