We study the problem of the rate of approximation in Orlicz spaces for a family of linear integral operators of the form (Twf)(s) = int_H Kw(s − hw(t))f(hw(t))dμH(t), w > 0, s \in G, where G and H are locally compact Hausdorff topological groups, f : G ! R is a measurable function, {hw}w>0 is a family of homeomorphisms hw : H --> G and {Kw}w>0, with Kw : G --> R, is a family of kernel functions. The general form of the operators allow us to give a unifying approach to the study of the rate of approximation for several classes of well-known integral operators, as the convolution ones, the Mellin convolution ones and a class of discrete operators, called ”generalized sampling series”, very important in the theory of signal processing. Moreover the setting of Orlicz spaces allows to deduce directly the results concerning the rate of approximation in Lp-spaces and this frame is also useful in the application to signal analysis since it gives the possibility to treat signals not necessarily bandlimited, nor with finite energy, as happens in the classical signal theory

Approximation in Orlicz spaces for linear integral operators and Applications

VINTI, Gianluca
2005

Abstract

We study the problem of the rate of approximation in Orlicz spaces for a family of linear integral operators of the form (Twf)(s) = int_H Kw(s − hw(t))f(hw(t))dμH(t), w > 0, s \in G, where G and H are locally compact Hausdorff topological groups, f : G ! R is a measurable function, {hw}w>0 is a family of homeomorphisms hw : H --> G and {Kw}w>0, with Kw : G --> R, is a family of kernel functions. The general form of the operators allow us to give a unifying approach to the study of the rate of approximation for several classes of well-known integral operators, as the convolution ones, the Mellin convolution ones and a class of discrete operators, called ”generalized sampling series”, very important in the theory of signal processing. Moreover the setting of Orlicz spaces allows to deduce directly the results concerning the rate of approximation in Lp-spaces and this frame is also useful in the application to signal analysis since it gives the possibility to treat signals not necessarily bandlimited, nor with finite energy, as happens in the classical signal theory
2005
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/113292
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