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CONSTRUCTIONS WITH ANALYTIC SEMIGROUPS AND ABSTRACT EXPONENTIAL DECAY RESULTS FOR EIGENFUNCTIONS
 

Summary: CONSTRUCTIONS WITH ANALYTIC SEMIGROUPS AND ABSTRACT
EXPONENTIAL DECAY RESULTS FOR EIGENFUNCTIONS
SIGURD ANGENENT
Presented on the occasion of H.Amann's 60th birthday
Contents
1. Introduction
2. Resolutions
3. Localization
4. An Example
5. Exponential decay of the resolvent
6. Exponential decay of eigenfunctions
7. Exponential decay in the example
8. Application to ``Fredholm solutions'' of Nonlinear Elliptic Systems
1. INTRODUCTION
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 ellip­
tic estimates for differential operators with continuous coefficients or H˜older­continuous
coefficients. As a side result we obtain an abstract exponential decay result for, say eigen­
functions corresponding to isolated eigenvalues.
After recalling some basic definitions in section 1.1 we first introduce a resolution of an

  

Source: Angenent, Sigurd - Department of Mathematics, University of Wisconsin at Madison

 

Collections: Mathematics