Müntz-Szász theorem with integral coefficients. II
HTML articles powered by AMS MathViewer
- by Le Baron O. Ferguson and Manfred von Golitschek PDF
- Trans. Amer. Math. Soc. 213 (1975), 115-126 Request permission
Abstract:
The classical Müntz-Szász theorem concerns uniform approximation on [0, 1] by polynomials whose exponents are taken from a sequence of real numbers. Under mild restrictions on the exponents or the interval, the theorem remains valid when the coefficients of the polynomials are taken from the integers.References
- David G. Cantor, On approximation by polynomials with algebraic integer coefficients. , Number Theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967) Amer. Math. Soc., Providence, R.I., 1969, pp. 1–13. MR 0257025
- Le Baron O. Ferguson, Approximation by polynomials with integral coefficients, Mathematical Surveys, No. 17, American Mathematical Society, Providence, R.I., 1980. MR 560902, DOI 10.1090/surv/017
- Le Baron O. Ferguson, Uniform approximation by polynomials with integral coefficients. I, II. , Pacific J. Math. 27 (1968), 53-69; ibid. 26 (1968), 273–281. MR 0236566, DOI 10.2140/pjm.1968.26.273
- Le Baron O. Ferguson, Müntz-Szász theorem with integral coefficients. I, Functional analysis and its applications (Internat. Conf., Eleventh Anniversary of Matscience, Madras, 1973; dedicated to Alladi Ramakrishnan), Lecture Notes in Math., Vol. 399, Springer, Berlin, 1974, pp. 119–122. MR 0430618
- Manfred von Golitschek, Erweiterung der Approximationssätze von Jackson im Sinne von Ch. Müntz. II, J. Approximation Theory 3 (1970), 72–86 (German). MR 257623, DOI 10.1016/0021-9045(70)90062-6 S. Kakeya, On approximate polynomials, Tôhoku Math. J. 6 (1914), 182-186. Ch. H. Müntz, Uber den Approximationssatz von Weierstrass, Math. Abhandlungen H. A. Schwarz zu seinem 50, Doktorjubiläum gewidmet, Berlin, 1914, pp. 303-312.
- Raymond E. A. C. Paley and Norbert Wiener, Fourier transforms in the complex domain, American Mathematical Society Colloquium Publications, vol. 19, American Mathematical Society, Providence, RI, 1987. Reprint of the 1934 original. MR 1451142, DOI 10.1090/coll/019
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 213 (1975), 115-126
- MSC: Primary 41A30
- DOI: https://doi.org/10.1090/S0002-9947-1975-0430619-3
- MathSciNet review: 0430619