Wyniki wyszukiwania

1

Tauberian theorems for vector-valued Fourier and Laplace transforms

100%

Chill R.

Studia Mathematica

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1998

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tom 128

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nr 1

55-69

EN

Let X be a Banach space and $f ∈ L^1_loc(ℝ;X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.

2

Stability of operator semigroups: ideas and results

63%

Chill R., Tomilov Y.

Banach Center Publications

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2007

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tom 75

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nr 1

71-109

3

Maximal regularity for second order non-autonomous Cauchy problems

51%

Batty C., Chill R., Srivastava S.

Studia Mathematica

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2008

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tom 189

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nr 3

205-223

EN

We consider some non-autonomous second order Cauchy problems of the form ü + B(t)u̇ + A(t)u = f(t ∈ [0,T]), u(0) = u̇(0) = 0. We assume that the first order problem u̇ + B(t)u = f(t ∈ [0,T]), u(0) = 0, has $L^{p}$-maximal regularity. Then we establish $L^{p}$-maximal regularity of the second order problem in situations when the domains of B(t₁) and A(t₂) always coincide, or when A(t) = κB(t).

Ograniczanie wyników

2 Studia Mathematica

1 Banach Center Publications

3 Chill R.

1 Batty C.

1 Srivastava S.

1 Tomilov Y.

1 2008

1 2007

1 1998

Tauberian theorems for vector-valued Fourier and Laplace transforms

Stability of operator semigroups: ideas and results

Maximal regularity for second order non-autonomous Cauchy problems