Hadamard's multiplication theorem - recent developments

Hermann Render

Colloquium Mathematicae (1997)

  • Volume: 74, Issue: 1, page 79-92
  • ISSN: 0010-1354

How to cite

top

Render, Hermann. "Hadamard's multiplication theorem - recent developments." Colloquium Mathematicae 74.1 (1997): 79-92. <http://eudml.org/doc/210503>.

@article{Render1997,
author = {Render, Hermann},
journal = {Colloquium Mathematicae},
keywords = {Hadamard product; coefficient multiplier; domain of efficient summability; commutative algebra; structure of prime ideals; semisimple, completely metrizable, locally convex algebra; topology of locally uniform convergence},
language = {eng},
number = {1},
pages = {79-92},
title = {Hadamard's multiplication theorem - recent developments},
url = {http://eudml.org/doc/210503},
volume = {74},
year = {1997},
}

TY - JOUR
AU - Render, Hermann
TI - Hadamard's multiplication theorem - recent developments
JO - Colloquium Mathematicae
PY - 1997
VL - 74
IS - 1
SP - 79
EP - 92
LA - eng
KW - Hadamard product; coefficient multiplier; domain of efficient summability; commutative algebra; structure of prime ideals; semisimple, completely metrizable, locally convex algebra; topology of locally uniform convergence
UR - http://eudml.org/doc/210503
ER -

References

top
  1. [1] S. Agmon, On the singularities of Taylor series with reciprocal coefficients, Pacific J. Math. 2 (1952), 431-453. Zbl0047.31201
  2. [2] N. U. Arakelyan, On efficient analytic continuation of power series, Math. USSR-Sb. 52 (1985), 21-39. Zbl0571.30003
  3. [3] L. Bieberbach, Analytische Fortsetzung, Ergeb. Math. Grenzgeb. 3, Springer, Berlin, 1955. 
  4. [4] R. P. Boas, Jr., Entire Functions, Academic Press, New York, 1954. Zbl66.0355.01
  5. [5] E. Borel, Sur les singularités des séries de Taylor, Bull. Soc. Math. France 26 (1898), 238-248. Zbl29.0210.03
  6. [6] R. M. Brooks, A ring of analytic functions, Studia Math. 24 (1964), 191-210. Zbl0199.46201
  7. [7] R. M. Brooks, A ring of analytic functions, II, ibid. 39 (1971), 199-208. Zbl0213.40303
  8. [8] R. Brück and J. Müller, Invertible elements in a convolution algebra of holomorphic functions, Math. Ann. 294 (1992), 421-438. Zbl0769.30002
  9. [9] R. Brück and J. Müller, Closed ideals in a convolution algebra of holomorphic functions, Canad. J. Math. 47 (1995), 915-928. Zbl0836.30002
  10. [10] P. L. Duren, Univalent Functions, Springer, Berlin, 1983. 
  11. [11] W. Fischer and I. Lieb, Funktionentheorie, Vieweg, Braunschweig, 1980. 
  12. [12] J. Hadamard, Théorème sur les séries entières, Acta Math. 22 (1899), 55-63. 
  13. [13] E. Hille, Analytic Function Theory, Vol. II, 2nd ed., Chelsea, New York, 1977. 
  14. [14] T. Husain, Multipliers of topological algebras, Dissertationes Math. 285 (1989). 
  15. [15] R. Larsen, Introduction to the Theory of Multipliers, Springer, Berlin, 1971. Zbl0213.13301
  16. [16] J. Müller, The Hadamard multiplication theorem and applications in summability theory, Complex Variables Theory Appl. 18 (1992), 75-81. 
  17. [17] J. Müller, Coefficient multipliers from H ( G 1 ) , into H ( G 2 ) , Arch. Math. (Basel) 61 (1993), 75-81. 
  18. [18] P. K. Raševskiĭ, Closed ideals in a countably generated normed algebra of analytic entire functions, Soviet Math. Dokl. 6 (1965), 717-719. 
  19. [19] R. Remmert, Funktionentheorie II, Springer, Berlin, 1991. 
  20. [20] H. Render, Homomorphisms on Hadamard algebras, Rend. Circ. Mat. Palermo (2) Suppl. 40 (1996), 153-158. Zbl0884.46035
  21. [21] H. Render, Topological algebras with an orthogonal total sequence, submitted. 
  22. [22] H. Render and A. Sauer, Algebras of holomorphic functions with Hadamard multiplication, Studia Math. 118 (1996), 77-100. 
  23. [23] H. Render and A. Sauer, Invariance properties of homomorphisms on algebras of holomorphic functions with Hadamard multiplication, ibid. 121 (1996), 53-65. Zbl0864.46029
  24. [24] H. Render and A. Sauer, Multipliers on vector spaces of holomorphic functions, submitted. 
  25. [25] H. H. Schaefer, Topological Vector Spaces, Springer, Berlin, 1971. 
  26. [26] S. Schottlaender, Der Hadamardsche Multiplikationssatz und weitere Kompositionssätze der Funktionentheorie, Math. Nachr. 11 (1954), 239-294. Zbl0059.06002
  27. [27] M. von Renteln, Ideale in Ringen ganzer Funktionen endlicher Ordnung, Mitt. Math. Sem. Giessen 95 (1972), 1-52. 
  28. [28] W. Żelazko, Banach Algebras, Elsevier, Amsterdam, 1973. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.