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Factorisation d'opérateurs différentiels à coefficients dans une extension liouvillienne d'un corps valué

Magali Bouffet (2002)

Annales de l’institut Fourier

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 ℂ ( ( z ) ) par un nombre fini d’exponentielles et de logarithmes algébriquement indépendants sur ℂ ( ( z ) ) .

Fine scales of decay of operator semigroups

Charles J. K. Batty, Ralph Chill, Yuri Tomilov (2016)

Journal of the European Mathematical Society

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...

Fourier multipliers for Hölder continuous functions and maximal regularity

Wolfgang Arendt, Charles Batty, Shangquan Bu (2004)

Studia Mathematica

Two operator-valued Fourier multiplier theorems for Hölder spaces are proved, one periodic, the other on the line. In contrast to the L p -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.

Functional-differential equations with Riemann-Liouville integrals in the nonlinearities

Milan Medveď (2014)

Mathematica Bohemica

A sufficient condition for the nonexistence of blowing-up solutions to evolution functional-differential equations in Banach spaces with the Riemann-Liouville integrals in their right-hand sides is proved. The linear part of such type of equations is an infinitesimal generator of a strongly continuous semigroup of linear bounded operators. The proof of the main result is based on a desingularization method applied by the author in his papers on integral inequalities with weakly singular kernels....

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