Hostname: page-component-76fb5796d-dfsvx Total loading time: 0 Render date: 2024-04-28T09:09:08.152Z Has data issue: false hasContentIssue false
  • English
  • Français

An application of Nevanlinna-pólya theorem to a cosine functional equation

Published online by Cambridge University Press:  09 April 2009

Hiroshi Haruki
Hiroshi Haruki
Affiliation:
Faculty of MathematicsUniversity of WaterlooWaterloo, Ontario, Canada
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We consider the cosine functional equation (see [1, 2, 3]) , where f(z) is an entire function of a complex variable z and x, y are complex variables.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 325 - 328
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Cauchy, A. L., Cours d'Analyse (Paris, 1821; Oeuvres Complètes (2), 3 (1897), 106–113).Google Scholar
[2]Flett, T. M., ‘Continuous solutions of the functional equation f(x+y)+f(x-y) = 2f(x)f(y)’, Amer. Math. Monthly 70 (1963), 392.Google Scholar
[3]Kaczmarz, S., ‘Sur l'équation fonctionnelle f(x)+f(x+y) = ϕ(y)f(x+y/2)’, Fund. Math. 6 (1924), 122–129.CrossRefGoogle Scholar
[4]Nevanlinna, R.Pólya, G., ‘Unitäre Transformationen analytischer Funktionen’, Jahresbericht der deutschen Mathematiker-Vereinigung 40 (1931) 80. (Aufgabe 103).Google Scholar
[5]Schmidt, H., ‘Lösung der Aufgabe 103’, Jahresbericht der deutschen Mathematiker-Vereinigung 43 (1934), 6–7.Google Scholar
[6]Pólya, G., Szegö, u. G., Aufgaben und Lehrsätze aus der Analysis (I, S. 94. Berlin-Göttingen-Heidelberg, Springer Verlag 1954).Google Scholar