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Generalized shift, generalized convolution and some extremal relations in the theory of the approximation of functions

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Abstract

One considers the generalized shift operator, defined on the space of functions, summable on [−1, 1] with the weight (1−x)∝(1+x)β(∞⩾β⩾−1/2), and the corresponding generalized convolution operator. One introduces some differential operators and one considers the corresponding classes of functions, which can be represented in the form of a generalized convolution. For these classes one obtains a series of extremal relations of the theory of approximation of functions by algebraic polynomials. An essential role is played by some duality relations for the classes of generalized convolutions.

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Authors
  1. S. Z. Rafal'son
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 150–157, 1986.

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Rafal'son, S.Z. Generalized shift, generalized convolution and some extremal relations in the theory of the approximation of functions. J Math Sci 42, 1646–1651 (1988). https://doi.org/10.1007/BF01665053

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  • DOI: https://doi.org/10.1007/BF01665053

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