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On démontre ici un lemme de Hensel pour les opérateurs différentiels. On en déduit un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension liouvillienne transcendante d’un corps valué. On obtient en particulier un
théorème de factorisation pour des opérateurs différentiels à coefficients dans une
extension de par un nombre fini d’exponentielles et de logarithmes
algébriquement indépendants sur .
Motivated by potential applications to partial differential equations, we develop a theory of fine scales of decay rates for operator semigroups. The theory contains, unifies, and extends several notable results in the literature on decay of operator semigroups and yields a number of new ones. Its core is a new operator-theoretical method of deriving rates of decay combining ingredients from functional calculus and complex, real and harmonic analysis. It also leads to several results of independent...
Two operator-valued Fourier multiplier theorems for Hölder spaces are proved, one periodic, the other on the line. In contrast to the -situation they hold for arbitrary Banach spaces. As a consequence, maximal regularity in the sense of Hölder can be characterized by simple resolvent estimates of the underlying operator.
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
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