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Added in proof (2 October 1961), ProfJ. Geronimus kindly called our attention to the paper ofJ. Shohat entitled “Application of orthogonal Tchebyscheff polynomials etc.”,Annali di Math., Ser. IV,18 (1939), pp. 201–238. Though this paper deals with problem of mean convergence,Shohat andTamarkin did not find it worth even quote in their book on Moment problem in 1943, though the book contains a detailed chapter on mechanical quadrature.
P. Erdős andP. Turán, On Interpolation. l,Annals of Math.,38 (1937), pp. 142–155. The essential relation (13) is stated there if only\(\int\limits_{ - 1}^1 {p(x)dx} \) exists andp(x)≧M owing to misprint: the letterM is to be replaced by O.
S. Bernstein, Leçons sur les propriétés extrémales etc., andS. Mandelbrojt, Séries adhérentes, régularisation des suites, applications, in part, p. 182.
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The content of this paper was the subject of a lecture we gave at the mathematical symposium of the Humboldt University, Berlin on 11 November 1960.
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Balázs, J., Turán, P. Notes on interpolation. VIII. Acta Mathematica Academiae Scientiarum Hungaricae 12, 469–474 (1964). https://doi.org/10.1007/BF02023929
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DOI: https://doi.org/10.1007/BF02023929