English

Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations

Dynamical Systems 2007-08-22 v2

Abstract

In this paper we present an extension of the Katznelson-Tzafriri Theorem to the asymptotic behavior of individual solutions of evolution equations u(t)=Au(t)+f(t)u'(t) =Au(t)+f(t). The obtained results do not require the uniform continuity of solutions as well as the well-posedness of the equations. The method of study is based on a recently developed approach to the spectral of functions that is direct and free of C_0-semigroups.

Cite

@article{arxiv.math/0703852,
  title  = {Katznelson-Tzafriri Type Theorems for Individual Solutions of Evolution Equations},
  author = {Nguyen Van Minh},
  journal= {arXiv preprint arXiv:math/0703852},
  year   = {2007}
}

Comments

This is the revised (and final) version of the version of March 28, 2007. This paper is to appear in the Proceedings of the A.M.S

R2 v1 2026-07-22T17:53:23.618Z