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Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions

100%
Domański P., Lindström M.
Annales Polonici Mathematici
|
2002
|
tom 79
|
nr 3
233-264
EN
We give an elementary approach which allows us to evaluate Seip's conditions characterizing interpolating and sampling sequences in weighted Bergman spaces of infinite order for a wide class of weights depending on the distance to the boundary of the domain. Our results also give some information on cases not covered by Seip's theory. Moreover, we obtain new criteria for weights to be essential.
2
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Algebras of real analytic functions: Homomorphisms and bounding sets

81%
Biström P., Jaramillo J. A., Lindström M.
Studia Mathematica
|
1995
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tom 115
|
nr 1
23-37
EN
This article deals with bounding sets in real Banach spaces E with respect to the functions in A(E), the algebra of real analytic functions on E, as well as to various subalgebras of A(E). These bounding sets are shown to be relatively weakly compact and the question whether they are always relatively compact in the norm topology is reduced to the study of the action on the set of unit vectors in $l_∞$ of the corresponding functions in $A(l_∞)$. These results are achieved by studying the homomorphisms on the function algebras in question, an idea that is also reversed in order to obtain new results for the set of homomorphisms on these algebras.
3
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Spectral properties of weighted composition operators on the Bloch and Dirichlet spaces

81%
Eklund T., Lindström M., Mleczko P.
Studia Mathematica
|
2016
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tom 232
|
nr 2
95-112
EN
The spectra of invertible weighted composition operators $uC_{φ}$ on the Bloch and Dirichlet spaces are studied. In the Bloch case we obtain a complete description of the spectrum when φ is a parabolic or elliptic automorphism of the unit disc. In the case of a hyperbolic automorphism φ, exact expressions for the spectral radii of invertible weighted composition operators acting on the Bloch and Dirichlet spaces are derived.
4
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Compact homomorphisms between algebras of analytic functions

81%
Aron R., Galindo P., Lindström M.
Studia Mathematica
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1997
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tom 123
|
nr 3
235-247
EN
We prove that every weakly compact multiplicative linear continuous map from $H^∞(D)$ into $H^∞(D)$ is compact. We also give an example which shows that this is not generally true for uniform algebras. Finally, we characterize the spectra of compact composition operators acting on the uniform algebra $H^∞(B_E)$, where $B_E$ is the open unit ball of an infinite-dimensional Banach space E.
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