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Almost-distribution cosine functions and integrated cosine functions

100%
Miana P.
Studia Mathematica
|
2005
|
tom 166
|
nr 2
171-180
EN
We introduce the notion of almost-distribution cosine functions in a setting similar to that of distribution semigroups defined by Lions. We prove general results on equivalence between almost-distribution cosine functions and α-times integrated cosine functions.
2
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Local and global solutions of well-posed integrated Cauchy problems

100%
Miana P.
Studia Mathematica
|
2008
|
tom 187
|
nr 3
219-232
EN
We study the local well-posed integrated Cauchy problem $v'(t) = Av(t) + (t^{α})/Γ(α+1)x$, v(0) = 0, t ∈ [0,κ), with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.
3
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Spectral mapping inclusions for the Phillips functional calculus in Banach spaces and algebras

63%
Fašangová E., Miana P.
Studia Mathematica
|
2005
|
tom 167
|
nr 3
219-226
EN
We investigate the weak spectral mapping property (WSMP) $\overline{μ̂(σ(A))} = σ(μ̂(A))$, where A is the generator of a 𝓒₀-semigroup in a Banach space X, μ is a measure, and μ̂(A) is defined by the Phillips functional calculus. We consider the special case when X is a Banach algebra and the operators $e^{At}$, t ≥ 0, are multipliers.
4
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Integrated version of the Post-Widder inversion formula for Laplace transforms

51%
Galé J., Martínez M., Miana P.
Studia Mathematica
|
2011
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tom 206
|
nr 2
161-173
EN
We establish an inversion formula of Post-Widder type for $λ^{α}$-multiplied vector-valued Laplace transforms (α > 0). This result implies an inversion theorem for resolvents of generators of α-times integrated families (semigroups and cosine functions) which, in particular, provides a unified proof of previously known inversion formulae for α-times integrated semigroups.
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