On the degree of convergence of extremal polynomials and other extremal functions

Walsh, J. L.; Sinclair, A.

doi:10.1090/S0002-9947-1965-0199419-X

On the degree of convergence of extremal polynomials and other extremal functions
HTML articles powered by AMS MathViewer

by J. L. Walsh and A. Sinclair

Trans. Amer. Math. Soc. 115 (1965), 145-160

DOI: https://doi.org/10.1090/S0002-9947-1965-0199419-X

PDF | Request permission

References

Variational methods in function theory

S. Ja. Al′per, Approximation of analytic functions in the mean over a region, Soviet Math. Dokl. 2 (1961), 36–39. MR 0116100

Zur Theorie und Praxis der konformen Abbildung

38

James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, DOI 10.1090/S0002-9947-1936-1501880-4
J. L. Doob, A minimum problem in the theory of analytic functions, Duke Math. J. 8 (1941), 413–424. MR 4885
O. J. Farrell, On approximation to an analytic function by polynomials, Bull. Amer. Math. Soc. 40 (1934), no. 12, 908–914. MR 1562998, DOI 10.1090/S0002-9904-1934-06002-6
P. R. Garabedian, The classes $L_p$ and conformal mapping, Trans. Amer. Math. Soc. 69 (1950), 392–415. MR 39072, DOI 10.1090/S0002-9947-1950-0039072-8
Olof Hanner, On the uniform convexity of $L^p$ and $l^p$, Ark. Mat. 3 (1956), 239–244. MR 77087, DOI 10.1007/BF02589410

Leçons sur la représentation conforme des aires simplement connexes

General mean modulus of analytic functions

3

Sur la représentation conforme

1

M. Keldych, Sur l’approximation en moyenne quadratique des fonctions analytiques, Rec. Math. [Mat. Sbornik] N.S. 5 (47) (1939), 391–401 (French, with Russian summary). MR 0002591
A. J. Macintyre and W. W. Rogosinski, Extremum problems in the theory of analytic functions, Acta Math. 82 (1950), 275–325. MR 36314, DOI 10.1007/BF02398280
Jacqueline Penez, Approximation by boundary values of analytic functions, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 240–243. MR 61163, DOI 10.1073/pnas.40.4.240

Über die Randwerte einer analytischen Funktion

W. W. Rogosinski and H. S. Shapiro, On certain extremum problems for analytic functions, Acta Math. 90 (1953), 287–318. MR 59354, DOI 10.1007/BF02392438

A division problem for analytic functions

W. E. Sewell, Degree of Approximation by Polynomials in the Complex Domain, Annals of Mathematics Studies, No. 9, Princeton University Press, Princeton, N. J., 1942. MR 0007054
Harold S. Shapiro, Applications of normed linear spaces to function-theoretic extremal problems, Lectures on functions of a complex variable, University of Michigan Press, Ann Arbor, Mich., 1955, pp. 399–404. MR 0070718

Sur les formules de Cauchy et de Green et quelques problèmes que s’y rattachent

7

A. Spitzbart, Approximation in the sense of least $p$th powers with a single auxiliary condition of interpolation, Bull. Amer. Math. Soc. 52 (1946), 338–346. MR 15483, DOI 10.1090/S0002-9904-1946-08579-1
J. L. Walsh, Interpolation and approximation by rational functions in the complex domain, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XX, American Mathematical Society, Providence, R.I., 1960. MR 0218587
J. L. Walsh, Note on invariance of degree of polynomial and trigonometric approximation under change of independent variable, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1528–1533. MR 123869, DOI 10.1073/pnas.45.10.1528
J. L. Walsh, Note on least-square approximation to an analytic function by polynomials, as measured by a surface integral, Proc. Amer. Math. Soc. 10 (1959), 273–279. MR 123725, DOI 10.1090/S0002-9939-1959-0123725-0
J. L. Walsh and H. G. Russell, Integrated continuity conditions and degree of approximation by polynomials or by bounded analytic functions, Trans. Amer. Math. Soc. 92 (1959), 355–370. MR 108595, DOI 10.1090/S0002-9947-1959-0108595-3
J. L. Walsh and H. G. Russel, On simultaneous interpolation and approximation by functions analytic in a given region, Trans. Amer. Math. Soc. 69 (1950), 416–439. MR 41212, DOI 10.1090/S0002-9947-1950-0041212-1
J. L. Walsh, Degree of polynomial approximation to an analytic function as measured by a surface integral, Proc. Nat. Acad. Sci. U.S.A. 48 (1962), 26–32. MR 132331, DOI 10.1073/pnas.48.1.26

Linear analysis