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Let be a semiprime ring with unity and , be automorphisms of . In this paper it is shown that if satisfies
for all and some fixed integer , then is an (, )-derivation. Moreover, this result makes it possible to prove that if admits an additive mappings satisfying the relations
for all and some fixed integer , then and are (, )derivations under some torsion restriction. Finally, we apply these purely ring theoretic results to semi-simple Banach algebras.
The aim is to investigate certain spectral properties, such as decomposability, the spectral mapping property and the Lyubich-Matsaev property, for linear differential operators with constant coefficients ( and more general Fourier multiplier operators) acting in . The criteria developed for such operators are quite general and p-dependent, i.e. they hold for a range of p in an interval about 2 (which is typically not (1,∞)). The main idea is to construct appropriate functional calculi: this is...
This paper is devoted to the homogenization beyond the periodic setting, of nonlinear monotone operators in a domain in with isolated holes of size ( a small parameter). The order of the size of the holes is twice that of the oscillations of the coefficients of the operator, so that the problem under consideration is a reiterated homogenization problem in perforated domains. The usual periodic perforation of the domain and the classical periodicity hypothesis on the coefficients of the operator...
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