Displaying similar documents to “On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions”

On the approximation by convolution operators in homogeneous Banach spaces on R^d

Draganov, Borislav (2014)

Mathematica Balkanica New Series

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AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20 The paper presents a description of the optimal rate of approximation as well as of a broad class of functions that possess it for convolution operators acting in the so-called homogeneous Banach spaces of functions on Rd. The description is the same in any such space and uses the Fourier transform. Simple criteria for establishing upper estimates of the approximation error via...

The intersection convolution of relations and the Hahn-Banach type theorems

Árpád Száz (1998)

Annales Polonici Mathematici

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By introducing the intersection convolution of relations, we prove a natural generalization of an extension theorem of B. Rodrí guez-Salinas and L. Bou on linear selections which is already a substantial generalization of the classical Hahn-Banach theorems. In particular, we give a simple neccesary and sufficient condition in terms of the intersection convolution of a homogeneous relation and its partial linear selections in order that every partial linear selection of this relation...

Mean-periodic operational calculi

Ivan Dimovski, Krystyna Skórnik (2000)

Banach Center Publications

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Elements of operational calculi for mean-periodic functions with respect to a given linear functional in the space of continuous functions are developed. Application for explicit determining of such solutions of linear ordinary differential equations with constant coefficients is given.

Convolutions related to q-deformed commutativity

Anna Kula (2010)

Banach Center Publications

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Two important examples of q-deformed commutativity relations are: aa* - qa*a = 1, studied in particular by M. Bożejko and R. Speicher, and ab = qba, studied by T. H. Koornwinder and S. Majid. The second case includes the q-normality of operators, defined by S. Ôta (aa* = qa*a). These two frameworks give rise to different convolutions. In particular, in the second scheme, G. Carnovale and T. H. Koornwinder studied their q-convolution. In the present paper we consider another convolution...

Homogenous Banach spaces on the unit circle.

Thomas Vils Pedersen (2000)

Publicacions Matemàtiques

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We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T. We apply our results to show that the algebra of all continuous functions on T is the only...