Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the zeros of total sets of polynomials


Authors: Philip Davis and Henry Pollak
Journal: Trans. Amer. Math. Soc. 72 (1952), 82-103
MSC: Primary 41.1X
MathSciNet review: 0045245
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Stefan Bergmann, Über die Entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthogonalfunktionen, Math. Ann. 86 (1922), no. 3-4, 238–271 (German). MR 1512089, http://dx.doi.org/10.1007/BF01457987
  • [2] R. P. Boas Jr., Basic sets of polynomials. I, Duke Math. J. 15 (1948), 717–724. MR 0026693 (10,187c)
  • [3] T. Carleman, Über die Approximation analytischer Funktionen durch lineare Aggregate von vorgegebenen Potenzen, Arkiv för Matematik, Astronomi, och Fysik vol. 17 (1922).
  • [4] G. Faber, Über polynomische Entwicklungen, Math. Ann. vol. 57 (1903).
  • [5] G. M. Golusin, Interior Problems of the Theory of Schlicht Functions, Office of Naval Research, Navy Department, Washington, D. C., 1947. Translated by T. C. Doyle, A. C. Schaeffer, and D. C. Spencer. MR 0020635 (8,575a)
  • [6] V. L. Goncharov, Teoriya Interpolirovaniya i Priblizheniyz Funktzii, Moscow-Leningrad, 1934.
  • [7] P. Korovkin, Sur une généralisation de la série de Taylor, C. R. (Doklady) Acad. Sci. URSS vol. 14 (1937).
  • [8] G. Pick, Über die konforme Abbildung eines Kreises auf ein schlichtes und zugleich beschränktes Gebiet, Sitzungsberichte der k. Akademie d. Wissenschaften, Vienna, Abt IIa, vol. 126 (1917) pp. 247-263.
  • [9] G. Szegö, Über orthogonale Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören, Math. Zeit. vol. 9 (1921).
  • [10] -, Orthogonal polynomials, Amer. Math. Soc. Colloquium Publications, vol. 23, New York, 1938.
  • [11] J. L. Walsh, Lemniscates and equipotential curves, Amer. Math. Monthly vol. 42 (1935).
  • [12] -, Interpolation and approximation by rational functions in the complex domain, Amer. Math. Soc. Colloquium Publications, vol. 20, New York, 1935.
  • [13] J. L. Walsh, On the Shape of Level Curves of Green’s Function, Amer. Math. Monthly 44 (1937), no. 4, 202–213. MR 1523908, http://dx.doi.org/10.2307/2300688
  • [14] J. M. Whittaker, Séries de base de polynomes quelconques, Collection Borel, Paris, 1949.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 41.1X

Retrieve articles in all journals with MSC: 41.1X


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1952-0045245-2
PII: S 0002-9947(1952)0045245-2
Article copyright: © Copyright 1952 American Mathematical Society