Constructions with Analytic Semigroups and Abstract Exponential Decay Results for Eigenfunctions
نویسنده
چکیده
In this note we present some constructions with generators of analytic semigroups which are an abstract version of the familiar method of “freezing the coefficients” to prove elliptic estimates for differential operators with continuous coefficients or Hölder-continuous coefficients. As a side result we obtain an abstract exponential decay result for, say eigenfunctions corresponding to isolated eigenvalues.
منابع مشابه
L1-estimates for eigenfunctions and heat kernel estimates for semigroups dominated by the free heat semigroup
We investigate selfadjoint positivity preserving C0-semigroups that are dominated by the free heat semigroup on Rd. Major examples are semigroups generated by Dirichlet Laplacians on open subsets or by Schrödinger operators with absorption potentials. We show explicit global Gaussian upper bounds for the kernel that correctly reflect the exponential decay of the semigroup. For eigenfunctions of...
متن کاملHigh order splitting methods for analytic semigroups exist
In this paper, we are concerned with the construction and analysis of high order exponential splitting methods for the time integration of abstract evolution equations which are evolved by analytic semigroups. We derive a new class of splitting methods of orders three to fourteen based on complex coefficients. An optimal convergence analysis is presented for the methods when applied to equation...
متن کاملEssential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
This paper is devoted to estimates of the exponential decay of eigenfunctions of difference operators on the lattice Zn which are discrete analogs of the Schrödinger, Dirac and square-root Klein-Gordon operators. Our investigation of the essential spectra and the exponential decay of eigenfunctions of the discrete spectra is based on the calculus of the so-called pseudodifference operators (i.e...
متن کاملAgmon-Type Exponential Decay Estimates for Pseudodifferential Operators∗
We study generalizations of Agmon-type estimates on eigenfunctions for Schrödinger operators. In the first part, we prove an exponential decay estimate on eigenfunctions for a class of pseudodifferential operators. In the second part, we study the semiclassical limit of ~-pseudodifferential operators, and exponential decay estimates on eigenfunctions and Briet-Combes-Duclos-type resolvent estim...
متن کاملFactorization of Non-symmetric Operators and Exponential H-theorem
We present an abstract method for deriving decay estimates on the resolvents and semigroups of non-symmetric operators in Banach spaces in terms of estimates in another smaller reference Banach space. This applies to a class of operators writing as a regularizing part, plus a dissipative part. The core of the method is a high-order quantitative factorization argument on the resolvents and semig...
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 1998