Interpolation of functions

by Szabados, J.

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Title Statements

Full title :Interpolation of functions / J. Szabados and P. Vértesi

Summary

I. Lagrange interpolation -- II. Some convergent interpolatory processes -- III. The Lebesgue function and Lebesgue function-type sums -- IV. Divergence of Lagrange interpolation -- V. Hermite-Fejer and Hermite-Fejer type interpolations -- VI. Comparison of Lagrange and Hermite-Fejer interpolations -- VII. Some problems in the theory of Lacunary interpolation -- VIII. Miscellaneous problems

This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics