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Explicit solutions for boundary value problems related to the operator equations X ( 2 ) - A X = 0

Lucas Jódar, Enrique A. Navarro (1991)

Applications of Mathematics

Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation X ( 2 ) - A X = 0 are studied for the general case, even when the algebraic equation X 2 - A = 0 is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.

Exponential expansiveness and complete admissibility for evolution families

Mihail Megan, Bogdan Sasu, Adina Luminiţa Sasu (2004)

Czechoslovak Mathematical Journal

Connections between uniform exponential expansiveness and complete admissibility of the pair ( c 0 ( , X ) , c 0 ( , X ) ) are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.

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

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