Advances in Differential Equations

A unifying approach to convergence of linear sampling type operators in Orlicz spaces

Gianluca Vinti and Luca Zampogni

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Abstract

In this paper we give a unified approach to the study of the convergence of a general family of linear sampling type operators which includes several operators very useful in signal reconstruction. We study both the pointwise and uniform convergence and the modular one in the general setting of Orlicz spaces. This creates the possibility of covering several settings such as $L^p$-spaces, the interpolation spaces, the exponential spaces and many others.

Article information

Source
Adv. Differential Equations Volume 16, Number 5/6 (2011), 573-600.

Dates
First available in Project Euclid: 17 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703301

Mathematical Reviews number (MathSciNet)
MR2816117

Zentralblatt MATH identifier
1223.41014

Subjects
Primary: 41A35: Approximation by operators (in particular, by integral operators) 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47A58: Operator approximation theory 47B38: Operators on function spaces (general) 94A12: Signal theory (characterization, reconstruction, filtering, etc.)

Citation

Vinti, Gianluca; Zampogni, Luca. A unifying approach to convergence of linear sampling type operators in Orlicz spaces. Adv. Differential Equations 16 (2011), no. 5/6, 573--600. https://projecteuclid.org/euclid.ade/1355703301.


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