ArticleOriginal scientific text
Title
Hadamard's multiplication theorem - recent developments
Authors 1
Affiliations
- Fachbereich Mathematik, Universität Duisburg, Lotharstr. 65, D-47057 Duisburg, Federal Republic of Germany
Keywords
Hadamard product, coefficient multiplier, domain of efficient summability
Bibliography
- S. Agmon, On the singularities of Taylor series with reciprocal coefficients, Pacific J. Math. 2 (1952), 431-453.
- N. U. Arakelyan, On efficient analytic continuation of power series, Math. USSR-Sb. 52 (1985), 21-39.
- L. Bieberbach, Analytische Fortsetzung, Ergeb. Math. Grenzgeb. 3, Springer, Berlin, 1955.
- R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954.
- E. Borel, Sur les singularités des séries de Taylor, Bull. Soc. Math. France 26 (1898), 238-248.
- R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210.
- R. M. Brooks, A ring of analytic functions, II, ibid. 39 (1971), 199-208.
- R. Brück and J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 294 (1992), 421-438.
- R. Brück and J. Müller, Closed ideals in a convolution algebra of holomorphic functions, Canad. J. Math. 47 (1995), 915-928.
- P. L. Duren, Univalent Functions, Springer, Berlin, 1983.
- W. Fischer and I. Lieb, Funktionentheorie, Vieweg, Braunschweig, 1980.
- J. Hadamard, Théorème sur les séries entières, Acta Math. 22 (1899), 55-63.
- E. Hille, Analytic Function Theory, Vol. II, 2nd ed., Chelsea, New York, 1977.
- T. Husain, Multipliers of topological algebras, Dissertationes Math. 285 (1989).
- R. Larsen, Introduction to the Theory of Multipliers, Springer, Berlin, 1971.
- J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables Theory Appl. 18 (1992), 75-81.
- J. Müller, Coefficient multipliers from
, into , Arch. Math. (Basel) 61 (1993), 75-81. - P. K. Raševskiĭ, Closed ideals in a countably generated normed algebra of analytic entire functions, Soviet Math. Dokl. 6 (1965), 717-719.
- R. Remmert, Funktionentheorie II, Springer, Berlin, 1991.
- H. Render, Homomorphisms on Hadamard algebras, Rend. Circ. Mat. Palermo (2) Suppl. 40 (1996), 153-158.
- H. Render, Topological algebras with an orthogonal total sequence, submitted.
- H. Render and A. Sauer, Algebras of holomorphic functions with Hadamard multiplication, Studia Math. 118 (1996), 77-100.
- H. Render and A. Sauer, Invariance properties of homomorphisms on algebras of holomorphic functions with Hadamard multiplication, ibid. 121 (1996), 53-65.
- H. Render and A. Sauer, Multipliers on vector spaces of holomorphic functions, submitted.
- H. H. Schaefer, Topological Vector Spaces, Springer, Berlin, 1971.
- S. Schottlaender, Der Hadamardsche Multiplikationssatz und weitere Kompositionssätze der Funktionentheorie, Math. Nachr. 11 (1954), 239-294.
- M. von Renteln, Ideale in Ringen ganzer Funktionen endlicher Ordnung, Mitt. Math. Sem. Giessen 95 (1972), 1-52.
- W. Żelazko, Banach Algebras, Elsevier, Amsterdam, 1973.