Skip to main content
Log in

The Hadamard Product on Open Sets in the Extended Plane

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

For two open sets Ω1, Ω2 in the extended complex plane, we define a Hadamard product as an operator from H1) × H2) to H1 * Ω2), where Ω1 * Ω2 is the so-called star product. Moreover, we study properties of this product and give applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Borel É.: Sur les singularités des séries de Taylor. Bulletin de la Société Mathématique de France 26, 238–248 (1898)

    MathSciNet  MATH  Google Scholar 

  2. Große-Erdmann K.-G.: On the Borel-Okada theorem and the Hadamard multiplication theorem. Complex Var. 22, 101–112 (1993)

    Article  MATH  Google Scholar 

  3. Hadamard J.: Théorème sur les séries entières. Acta Math. 22, 55–63 (1899)

    Article  MathSciNet  Google Scholar 

  4. Hille E.: Analytic Function Theory Volume II. Chelsea Publishing Company, New York (1962)

    Google Scholar 

  5. Levin B.Y.: Lectures on Entire Functions. American Mathematical Society, Providence (1996)

    MATH  Google Scholar 

  6. Müller J.: The Hadamard multiplication theorem and applications in summability theory. Complex Var. 18, 155–166 (1992)

    Article  MATH  Google Scholar 

  7. Pólya G.: Untersuchungen über Lücken und Singularitäten von Potenzreihen. II. Ann. Math. 2(34), 731–777 (1933)

    Google Scholar 

  8. Powell R.E.: Summability Theory and its Applications. Van nost Reinhold, New York (1973)

    Google Scholar 

  9. Rudin W.: Real and Complex Analysis, 3rd edn. McGraw-Hill, New York (1987)

    MATH  Google Scholar 

  10. Yosida K.: Functional Analysis, 6th edn. Springer, Berlin (1980)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to J. Müller.

Additional information

Communicated by Victor Katsnelson.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Müller, J., Pohlen, T. The Hadamard Product on Open Sets in the Extended Plane. Complex Anal. Oper. Theory 6, 257–274 (2012). https://doi.org/10.1007/s11785-010-0085-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11785-010-0085-2

Keywords

Mathematics Subject Classification (2000)

Navigation