Displaying similar documents to “Developments from nonharmonic Fourier series.”

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

Paweł Domański, Mikael Lindström (2002)

Annales Polonici Mathematici

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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.

The class Bpfor weighted generalized Fourier transform inequalities

Chokri Abdelkefi, Mongi Rachdi (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In the present paper, we prove weighted inequalities for the Dunkl transform (which generalizes the Fourier transform) when the weights belong to the well-known class Bp. As application, we obtain the Pitt’s inequality for power weights.

Sampling and interpolation in the Paley-Wiener spaces L , 0 < p ≤ 1.

Kristin M. Flornes (1998)

Publicacions Matemàtiques

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Following Beurling's ideas concerning sampling and interpolation in the Paley-Wiener space L , we find necessary and sufficient density conditions for sets of sampling and interpolation in the Paley-Wiener spaces L for 0 < p ≤ 1.

Sampling measures.

Joaquim Ortega-Cerdà (1998)

Publicacions Matemàtiques

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We give a description of all measures such that for any function in a weighted Fock spaces the L norm with respect to the measure is equivalent to the usual norm in the space. We do so by a process of discretization that reduces the problem to the description of sampling sequences. The same kind of result holds for weighted Bergman spaces and the Paley-Wiener space.