Remarks on Besov spaces and best polynomial approximation

Ditzian, Z.; Totik, V.

doi:10.1090/S0002-9939-1988-0969047-5

Remarks on Besov spaces and best polynomial approximation
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by Z. Ditzian and V. Totik PDF

Proc. Amer. Math. Soc. 104 (1988), 1059-1066 Request permission

Abstract:

Besov-type spaces that are generated by new moduli of smoothness are related to sequence spaces of $\left \{ {{E_n}\left ( f \right )} \right \}$ where ${E_n}\left ( f \right )$ is the appropriate best algebraic polynomial approximation.

References

Paul L. Butzer and Hubert Berens, Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften, Band 145, Springer-Verlag New York, Inc., New York, 1967. MR 0230022
Paul L. Butzer and Karl Scherer, Approximationsprozesse und Intepolationsmethoden, B. I. Hochschulskripten, vol. 826/826, Bibliographisches Institut, Mannheim-Zürich, 1968 (German). MR 0259461
Ronald A. DeVore, Sherman D. Riemenschneider, and Robert C. Sharpley, Weak interpolation in Banach spaces, J. Functional Analysis 33 (1979), no. 1, 58–94. MR 545385, DOI 10.1016/0022-1236(79)90018-1
R. A. DeVore and V. A. Popov, Interpolation spaces and nonlinear approximation, Function spaces and applications (Lund, 1986) Lecture Notes in Math., vol. 1302, Springer, Berlin, 1988, pp. 191–205. MR 942269, DOI 10.1007/BFb0078875
Z. Ditzian and V. Totik, Moduli of smoothness, Springer Series in Computational Mathematics, vol. 9, Springer-Verlag, New York, 1987. MR 914149, DOI 10.1007/978-1-4612-4778-4
Gen-ichirô Sunouchi, Derivatives of a trigonometric polynomial of best approximation, Abstract Spaces and Approximation (Proc. Conf., Oberwolfach, 1968) Birkhäuser, Basel, 1969, pp. 233–241. MR 0264308