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by Polynomials T. Erdélyi, Paul Erdős, Paul Erdős, Interpolation P. Vértesi
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Abstract:
at Kerepesi Cemetery in Budapest to pay their last respects to Paul Erdős. If there was one theme suggested by the farewell orations, it was that the world of mathematics had lost a legend, one of its great representatives. On October 21, 1996, in accordance with his last wishes, Paul Erdős ’ ashes were buried in his parents ’ grave at the Jewish cemetery on Kozma street in Budapest. Paul Erdős was one of this century’s greatest and most prolific mathematicians. He is said to have written about 1500 papers, with almost 500 co-authors. He made fundamental contributions in numerous areas of mathematics. There is a Hungarian saying to the effect that one can forget everything but one’s first love. When considering Erdős and his mathematics, we cannot speak of “first love”, but of “first loves”, and approximation theory was among them. Paul Erdős wrote more than 100 papers that are connected, in one way or another, with the approximation of functions. In these two short reviews, we try to present some of Paul’s fundamental contributions to approximation theory. A list of Paul’s papers in approximation theory is given at the end of this article.
Citations
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20
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Etude des Sommes d’Exponentielles
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18
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les polynômes á coefficients unimodulaires
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- 1980
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17
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Uber die interpolatorische Darstellung stetiger Funktionen
– Faber
- 1978
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11
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On the Lebesgue function for polynomial interpolation
– Brutman
- 1997
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7
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A characterization of the Lagrange interpolating projection with minimal Tchebycheff norm
– Kilgore
- 1978
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6
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On the Erdos conjecture concerning minimal norm interpolation on the unit circle
– Brutman, Pinkus
- 1980
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5
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Proof of the conjectures of Bernstein and Erdos concerning the optimal nodes for polynomial interplation
– Boor, Pinkus
- 1978
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5
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A Survey on Mean Convergence of Interpolatory Processes
– Szabados, Vertesi
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4
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Nikolskii- and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros
– Erdélyi, Remez-
- 1992
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4
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Optimal Lebesgue constant for Lagrange interpolation
– Vértesi
- 1990
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3
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Proof of a conjecture of Erdős about the longest polynomial
– Bojanov
- 1982
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3
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The arc length of the lemniscate (|p(z
– Borwein
- 1995
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3
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Sur les fonctions bornées et integrables
– Fejér
- 1900
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3
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Evaluation of lebesgue constants
– Gunttner
- 1980
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3
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Some inequalities for algebraic and trigonometric polynomials
– Kristiansen
- 1979
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2
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Mean convergence of orthogonal series and Lagrange interpolation
– Askey
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2
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On the theory of interpolation
– Grünwald
- 1943
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2
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Proof of a polynomial conjecture
– Kristiansen
- 1974
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2
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The coefficients of cyclotomic polynomials
– Maier
- 1990
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2
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Cyclotomic polynomials with large coefficients
– Maier
- 1993
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2
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Sur la divergence des polynômes d’interpolation
– Marcinkiewicz
- 1937
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2
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Coefficient and intergal mean estimates for algebraic and trigonometric polynomials with restricted zeros
– Saff, Sheil-Small
- 1974
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2
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On the norms of interpolating operators
– Shekhtman
- 1988
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2
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On a problem of Erdős in Diophantine approximation
– Wagner
- 1980
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1
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la limitation des valeurs d’une polynôme Pn(x) dedegrénsur tout un segment par ses valeurs en n + 1 points du segment, Izv
– Bernstein, Sur
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1
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Über Interpolation, Göttinger Nachrichten
– Fejér
- 1916
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1
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Lebeguesche Konstanten und divergente Fourierreihen, Journ. für Reine und Angew
– Fejér
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1
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Über Divergenzerscheinungen der Lagrangeschen Interpolationspolynome
– Grünwald
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1
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Approximation durch trigonometrische Interpolation, Diplomarbeit (Technische Universität Hannover
– Günttner
- 1970
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1
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The “coarse and fine theory of interpolation” of Erdos and Turan in a broader view, Const
– Halasz
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1
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The spaces � C∗ ω and � C∗ ω and the convergence of interpolation processes in them (in Russian), Doklady Akad
– Lozinskii
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1
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Sur l’interpolation
– Marcinkiewicz
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1
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Orthogonal Polynomials, Memoirs AMS,Vol
– Nevai
- 1979
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1
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On the norm of certain interpolating operators
– Szabados
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1
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Timan, Approximation Theory of Functions of a Real Variable (in Russian
– F
- 1960
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1
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On sums of Lebesgue function type
– Vértesi
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1
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On the optimal Lebesgue constants for polynomial interpolation
– Vértesi
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