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Some problems concerning different types of vector valued almost periodic functions

100%

Basit B.

Instytut Matematyczny Polskiej Akademii Nauk

EN

Abstract We study some problems concerning derivatives and indefinite integrals of elements of wide classes of functions (including almost periodic, recurrent, almost automorphic and Eberlein almost periodic functions). We introduce a notion of a spectrum of a function with respect to a class of functions. This notion enables us to investigate almost periodicity of the bounded solutions of certain functional equations.

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Strong continuity of semigroup homomorphisms

61%

Basit B., Pryde A.

Studia Mathematica

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1999

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tom 132

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nr 1

71-78

EN

Let J be an abelian topological semigroup and C a subset of a Banach space X. Let L(X) be the space of bounded linear operators on X and Lip(C) the space of Lipschitz functions ⨍: C → C. We exhibit a large class of semigroups J for which every weakly continuous semigroup homomorphism T: J → L(X) is necessarily strongly continuous. Similar results are obtained for weakly continuous homomorphisms T: J → Lip(C) and for strongly measurable homomorphisms T: J → L(X).

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Differences of functions in locally convex spaces and applications to almost periodic and almost automorphic functions

61%

Basit B., Emam M.

Annales Polonici Mathematici

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1983

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tom 41

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nr 3

193-201

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Studia Mathematica

3 Basit B.

1 Emam M.

1 Pryde A.

1 1999

1 1995

1 1983

Some problems concerning different types of vector valued almost periodic functions

Strong continuity of semigroup homomorphisms

Differences of functions in locally convex spaces and applications to almost periodic and almost automorphic functions