GROWTH OF THE ANALYTIC FUNCTION ON THE DISC
Abstract
In this article, the order of exponential of growth of analytical function ϕ on the disc is introduced, and the relation between the order of the function ϕ and its coefficients is obtained. An application of this result gives us the description of the behavior of the resolvent R(B,λ) of linear bounded operator where λ approaches the spectrum.
About the Authors
A. B. ANTONEVICH
Belarusian State University
Belarus
Belarus
ALI A. SHUKUR
Belarusian State University
Belarus
Belarus
References
1. Holland, A. S. B. Introduction to the theory of Entire functions / A. S. B. Holland. – New York; London: Academic press, 1973.
2. Маркушевич, А. И. Теория аналитических функций / А. И. Маркушевич. – Москва, 1950.
3. Евграфов, М. А. Асимптотические оценки и целые функции / М. А. Евграфов. – Москва, 1957.
4. Faber, G. Beitrag zur Theorie der ganzen funktionen / G. Faber // Math. Ann. – 1911. – Vol. 70. – P. 48–68.
5. Bieberbach, L. Analytische Fortsetzung / L. Bieberbach. – Springer Verlag, 1955.
6. Nagy, B. A resolvent condition implying power boundedness / B. Nagy, J. A. Zemanek // Studia Math. – 1999. – Vol. 134. – P. 143–151.
7. Nevanlinna, O. Resolvent conditions and powers of operators / O. Nevanlinna // Studia Math. – 2011. – Vol. 145. – P. 113–134.
8. Nevanlinna, O. On the growth of the resolvent operators for power bounded operators / O. Nevanlinna // Banach center publiction. – 1997. – Vol. 28. – P. 247–264.
9. Zabreko, P. P. Error estimates of successive approximations and spectral properties of linear operators / P. P. Zabreko // Numercal functional analysis and optimizаtion. – 1990. – Vol. 7–8. – P. 823–838.
10. Антоневич, А. Б. Оценка резольвент для дискретных взвешенного операторов / А. Б. Антоневич, Али А. Шукур // Проблемы физики, математики и техники. – 2015. – № 22. – С. 48–52.
11. Antonevich, A. B. Linear functional equation.operator approach / A. B. Antonevich. – Birkhauser, 1996.
Review
Views: 757
Email this article 