Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-21T14:40:59.555Z Has data issue: false hasContentIssue false
  • English
  • Français

Representation Formulas for Integrable and Entire Functions of Exponential Type II

Published online by Cambridge University Press:  20 November 2018

Clément Frappier
Clément Frappier*
Affiliation:
Département de mathématiques appliquées Ecole Polytechnique de Montréal Campus de l'Université de Montréal Case postale 6079, Succursale “A “ Montréal, Quebec H3C 3A7
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 adopt the terminology and notations of [5]. If f ∈ Bτ is an entire function of exponential type τ bounded on the real axis then we have the complementary interpolation formulas [1, p. 142-143]

and

where t, γ are reals and

Keywords

30D1041A0542A05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 1 , 01 February 1991 , pp. 34 - 47
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Achieser, N.I., Theory of approximation. Frederick Ungar Publishing Co.,New York, 1956.Google Scholar
2. Apostol, T.M., Introduction to analytic number theory. Springer-Verlag, New York, 1976.Google Scholar
3. Boas, R.P., Entire functions. Academic Press, New York, 1954.Google Scholar
4. Frappier, C., Some representation formulas for entire functions of exponential type, Bull. Austr. Math. Soc. 37(1988), 17–26.Google Scholar
5. Frappier, C., Representation formulas for integrable and entire functions of exponential type I, Can. J. Math., No.4XL(1988), 1010–1024.Google Scholar
6. Hörmander, L., Some inequalities for functions of exponential type, Math. Scand. 3(1955), 21–27.Google Scholar
7. Macintyre, A.J., Laplace's transformation and integral functions, Proc. London Math. Soc. 45(1939), 1–20.Google Scholar
8. Nikol'skii, S.M., Approximation of functions of several variables and imbedding theorems. Springer-Verlag, New York, 1975.Google Scholar
9. Olivier, P. et Rahman, Q.I., Sur une formule de quadrature pour des fonctions entières, RAIRO Modél. Math. Anal. Numér. 20(1986), 517–537.Google Scholar
10. Rahman, Q.I., On asymmetric entire functions II, Math. Ann. 167(1966), 49–52.Google Scholar