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M\"untz Spaces and Remez Inequalities
Author(s):
Peter
Borwein;
Tam\'as
Erd\'elyi
Journal:
Bull. Amer. Math. Soc.
32
(1995),
38-42.
MSC (1991):
Primary 41A17;
Secondary 30B10, 26D15
MathSciNet review:
1273395
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Additional information
References:
- [1]
- J. M. Anderson, M\"untz-Sz\'asz type approximation and the angular growth of lacunary integral functions, \amstran \textbf{169} (1972), 237--248. MR 310259
- [2]
- J. Bak and D. J. Newman, Rational combinations of $x^{\lambda _k}, \lambda _k \geq 0$, are always dense in $C[0,1]$, \jat \textbf{23} (1978), 155--157. MR 487180
- [3]
- S. N. Bernstein, Collected works\,\RM : Vol \RM 1. Constructive theory of functions \rm (1905-1930), English translation, Atomic Energy Commission, Springfield, Virginia, 1958.
- [4]
- R. P. Boas, Entire functions, Academic Press, New York, 1954. MR 68627
- [5]
- P. B. Borwein, Zeros of Chebyshev polynomials in Markov systems, J. Approx. Theory \textbf{63} (1990), 56--64. MR 1074081
- [6]
- P. B. Borwein, Variations on M\"untz\RM 's theme, Canad. Math. Bull. \textbf{34} (1991), 305--310. MR 1127751
- [7 ]
- P. B. Borwein and T. Erd\'elyi , Notes on lacunary M\"untz polynomials, Israel J. Math. \textbf{76} (1991), 183--192. MR 1177339
- [8]
- , Lacunary M\"untz systems, Proc. Edinburgh Math. Soc. (2) \textbf{36} (1993), 361--374. MR 1242750
- [9]
- , Polynomials and polynomials inequalities, Springer-Verlag, New York.
- [10 ]
- P. B. Borwein, T. Erd\'elyi, and J. Zhang , M\"untz systems and orthogonal M\"untz-Legendre polynomials, Trans. Amer. Math. Soc. {\bf 342} (1994), 523--542. MR 1227091
- [11]
- E. W. Cheney, Introduction to approximation theory, McGraw-Hill, New York, 1966. MR 222517
- [12]
- J. A. Clarkson and P. Erd\H os, Approximation by polynomials, Duke Math. J. \textbf{10} (1943), 5--11. MR 7813
- [13]
- T. Erd\'elyi, Remez-type inequalities on the size of generalized polynomials, J. London Math. Soc. (2) \textbf{45} (1992), 255--264. MR 1171553
- [14]
- T. Erd\'elyi, Remez type inequalities and their applications, J. Comput. Appl. Math. \textbf{47} (1993), 167--210. MR 1237312
- [15]
- G. Freud, Orthogonal polynomials, Pergamon Press, Oxford, 1971.
- [16 ]
- W. A. J. Luxemburg and J. Korevaar , Entire functions and M\"untz-Sz\'asz type approximation, Trans. Amer. Math. Soc. \textbf{157} (1971), 23--37. MR 281929
- [17]
- C. M\"untz, \"Uber den Approximationsatz von Weierstrass, H. A. Schwartz Festschrift, Berlin, 1914.
- [18]
- D. J. Newman, Derivative bounds for M\"untz polynomials, J. Approx. Theory \textbf{18} (1976), 360--362. MR 430604
- [19]
- D. J. Newman, \emph{Approximation with rational functions}, Amer. Math. Soc., Providence, RI, 1978. MR 539314
- [20]
- E. J. Remez, Sur une propri\'et\'e des polyn\^omes de Tchebyscheff, Comm. Inst. Sci. Kharkow \textbf{13} (1936), 93--95.
- [21]
- T. J. Rivlin, Chebyshev polynomials, \rm 2nd ed., Wiley, New York, 1990. MR 1060735
- [22]
- L. Schwartz, Etude des sommes d'exponentielles, Hermann, Paris, 1959. MR 106383
- [23]
- G. Somorjai, A M\"untz-type problem for rational approximation, Acta. Math. Hungar. \textbf{27} (1976), 197--199. MR 430617
- [24]
- O. Sz\'asz, \"Uber die Approximation steliger Funktionen durch lineare Aggregate von Potenzen, Math. Ann. \textbf{77} (1916), 482--496. MR 1511875
- [25]
- G. Szeg\H o, On the density of quotients of lacunary polynomials, Acta Math. Hungar. \textbf{30} (1922), 149--154. MR 454462
- [26]
- A. K. Taslakyan, Some properties of Legendre quasi-polynomials with respect to a M\"untz system, Mathematics \textbf{2} (1984), 179--189 \afterall (Russian, Armenian summary). MR 875260
- [27]
- M. von Golitschek, A short proof of M\"untz Theorem, J. Approx. Theory \textbf{39} (1983), 394--395. MR 723231
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Additional Information:
DOI:
10.1090/S0273-0979-1995-00553-7
PII:
S 0273-0979(1995)00553-7
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