We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney (regularized long-wave), Korteweg-deV...

We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping theorem are discussed. The construction is illustrated by a simple example of calculus and joint spectrum of two non-commuting selfadjoint n× n matrices.

We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for £-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.

For a strongly continuous semigroup (T (t))t≥0 with generator A we introduce its critical spectrum σcrit(T (t)). This yields in an optimal way the spectral mapping theorem σ(T (t)) = e ∪ σcrit(T (t)) and improves classical stability results.

In this article we give some characterizations of exponential stability for a periodic discrete evolution family of bounded linear operators acting on a Banach space in terms of discrete evolution semigroups, acting on a special space of almost periodic sequences. As a result, a spectral mapping theorem is stated. AMS (MOS) Subject Classification Codes: Primary 35B35.

in this paper, genetic programming is applied for quality improvement of noisy speech signal. therefore, a system including both spectral subtraction and genetic programming is implemented for speech enhancement. in the proposed method, first noise is reduced by spectral subtraction. in the next step, genetic programming trees are trained for more enhancement of noisy signal by mapping the sign...

binayak et al in [1] proved a fixed point of generalized kannan type-mappings in generalized menger spaces. in this paper we extend gen- eralized kannan-type mappings in generalized fuzzy metric spaces. then we prove a fixed point theorem of this kind of mapping in generalized fuzzy metric spaces. finally we present an example of our main result.