Distribution semigroups and one parameter semigroups

• Autorzy: Kisyński J.
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space, and S an L(X)-valued pre-distribution semigroup in the sense of P. C. Kunstmann [15]. Let X[infinity] be the space of [C^infinity] vectors for S. Assume that X[infinity is not equal to ]{0}. Equipped with a natural topology, X[infinity] is a Frechet space continuously imbedded into X. It is proved that there is a unique operator semigroup (St)[t belongs to R] +[is a subset of] L(X[infinity]) with [C^infinity] trajectories such that S(phi)x = [...] for every x [belongs to] X[infinity] and every [phi belongs to] D(R). Furthermore, it is shown that X[infinity] = [...], where [...] is the set of finite sums of elements of the form S(phi)x, x [belongs to] X, [phi belongs to] D(R), sup[phi is a subset of R+].

Słowa kluczowe

EN

Carding space; convolution; distribution semigroup; fundamental solution (for a linear differential equation in a Banach space); generator; infinitely differentiable vectors; pseudoresolvent of polynomial growth in a logarithmic region

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 2
• Strony: 189--216
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Kisyński J.

• Technical University of Lublin, Nadbystrzycka 38D, P.O. Box 189, 20-618 Lublin, Poland,

Bibliografia

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