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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

A conjecture of M. Golomb on optimal and nearly-optimal linear approximation


Authors: Wolfgang Dahmen and Ernst Gorlich
Journal: Bull. Amer. Math. Soc. 80 (1974), 1199-1202
MSC (1970): Primary 42A08; Secondary 41A25, 41A35, 41A50
MathSciNet review: 0355447
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  • 1. D. L. Berman, On the impossibility of constructing a linear polynomial operator furnishing an approximation of the order of the best approximation, Dokl. Akad. Nauk SSSR 120 (1958), 1175–1177 (Russian). MR 0098941 (20 #5387)
  • 2. E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0222517 (36 #5568)
  • 3. Michael Golomb, Optimal and nearly-optimal linear approximations, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964), Elsevier Publ. Co., Amsterdam, 1965, pp. 83–100. MR 0201889 (34 #1767)
  • 4. G. H. Hardy and J. E. Littlewood, Some new properties of fourier constants, Math. Ann. 97 (1927), no. 1, 159–209. MR 1512359, http://dx.doi.org/10.1007/BF01447865
  • 5. J. Marcinkiewicz, Quelques remarques sur l'interpolation, Acta Litt. Acad. Sci. Szeged 8 (1937), 127-130.
  • 6. S. M. Nikol′skiĭ, On linear methods of summation of Fourier series, Izvestiya Akad. Nauk SSSR. Ser. Mat. 12 (1948), 259–278 (Russian). MR 0027084 (10,247b)
  • 7. N. A. Sapogov, On the norms of linear polynomial operators, Dokl. Akad. Nauk SSSR 143 (1962), 1286–1288 (Russian). MR 0136921 (25 #381b)
  • 8. S. Sidon, Über Fourier-Koeffizienten, J. London Math. Soc. 13 (1938), 181-183.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1974-13676-1
PII: S 0002-9904(1974)13676-1