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Some convergence results on sinc interpolation. (English) Zbl 1069.41005

Summary: This paper is devoted to the investigation of sine interpolation properties corresponding to a sequence of functions having the sine function as a basis, the interpolation is taken over the dyadic partition of the interval \([0,2\pi]\). In particular, a new class of functions for which the interpolation converge is introduced. The convergence of our interpolation processes is studied and answered in quite a comprehensive way. In fact, the paper aims to provide a guideline towards a large number of problems of interest in applied sciences.

MSC:

41A05 Interpolation in approximation theory
41A10 Approximation by polynomials
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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