ArticleOriginal scientific text

Title

Hadamard's multiplication theorem - recent developments

Authors 1

Affiliations

  1. Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, D-47057 Duisburg, Federal Republic of Germany

Keywords

Hadamard product, coefficient multiplier, domain of efficient summability

Bibliography

  1. S. Agmon, On the singularities of Taylor series with reciprocal coefficients, Pacific J. Math. 2 (1952), 431-453.
  2. N. U. Arakelyan, On efficient analytic continuation of power series, Math. USSR-Sb. 52 (1985), 21-39.
  3. L. Bieberbach, Analytische Fortsetzung, Ergeb. Math. Grenzgeb. 3, Springer, Berlin, 1955.
  4. R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954.
  5. E. Borel, Sur les singularités des séries de Taylor, Bull. Soc. Math. France 26 (1898), 238-248.
  6. R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210.
  7. R. M. Brooks, A ring of analytic functions, II, ibid. 39 (1971), 199-208.
  8. R. Brück and J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 294 (1992), 421-438.
  9. R. Brück and J. Müller, Closed ideals in a convolution algebra of holomorphic functions, Canad. J. Math. 47 (1995), 915-928.
  10. P. L. Duren, Univalent Functions, Springer, Berlin, 1983.
  11. W. Fischer and I. Lieb, Funktionentheorie, Vieweg, Braunschweig, 1980.
  12. J. Hadamard, Théorème sur les séries entières, Acta Math. 22 (1899), 55-63.
  13. E. Hille, Analytic Function Theory, Vol. II, 2nd ed., Chelsea, New York, 1977.
  14. T. Husain, Multipliers of topological algebras, Dissertationes Math. 285 (1989).
  15. R. Larsen, Introduction to the Theory of Multipliers, Springer, Berlin, 1971.
  16. J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables Theory Appl. 18 (1992), 75-81.
  17. J. Müller, Coefficient multipliers from H(G1), into H(G2), Arch. Math. (Basel) 61 (1993), 75-81.
  18. P. K. Raševskiĭ, Closed ideals in a countably generated normed algebra of analytic entire functions, Soviet Math. Dokl. 6 (1965), 717-719.
  19. R. Remmert, Funktionentheorie II, Springer, Berlin, 1991.
  20. H. Render, Homomorphisms on Hadamard algebras, Rend. Circ. Mat. Palermo (2) Suppl. 40 (1996), 153-158.
  21. H. Render, Topological algebras with an orthogonal total sequence, submitted.
  22. H. Render and A. Sauer, Algebras of holomorphic functions with Hadamard multiplication, Studia Math. 118 (1996), 77-100.
  23. H. Render and A. Sauer, Invariance properties of homomorphisms on algebras of holomorphic functions with Hadamard multiplication, ibid. 121 (1996), 53-65.
  24. H. Render and A. Sauer, Multipliers on vector spaces of holomorphic functions, submitted.
  25. H. H. Schaefer, Topological Vector Spaces, Springer, Berlin, 1971.
  26. S. Schottlaender, Der Hadamardsche Multiplikationssatz und weitere Kompositionssätze der Funktionentheorie, Math. Nachr. 11 (1954), 239-294.
  27. M. von Renteln, Ideale in Ringen ganzer Funktionen endlicher Ordnung, Mitt. Math. Sem. Giessen 95 (1972), 1-52.
  28. W. Żelazko, Banach Algebras, Elsevier, Amsterdam, 1973.
Pages:
79-92
Main language of publication
English
Received
1996-11-27
Published
1997
Exact and natural sciences