A representation theorem and approximation operators arising from inequalities involving differential operators

Author:
D. Leviatan

Journal:
Trans. Amer. Math. Soc. **168** (1972), 85-99

MSC:
Primary 41A35

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296573-X

MathSciNet review:
0296573

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Abstract | References | Similar Articles | Additional Information

Abstract: A representation of functions as integrals of a kernel , which was introduced by Studden, with respect to functions of bounded variation in is obtained whenever the functions satisfy some conditions involving the differential operators . The results are related to the concepts of generalized completely monotonic functions and generalized absolutely monotonic functions in . Some approximation operators for the approximation of continuous functions in arise naturally and are introduced; some sequence-to-function summability methods are also introduced.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296573-X

Keywords:
Generalized completely monotonic functions,
representation of functions as integrals of a kernel,
approximation operators in ,
sequence-to-function summability methods

Article copyright:
© Copyright 1972
American Mathematical Society