Generalization of Liouville’s theorem
Keywords:
Liouville’s theorem; Taylor series; Laurent series; bounded function; entire functionAbstract
The Liouville’s theorem and its proof as an important element in the study of entire functions are present in this paper. An interpretation of this theorem through the Bessel function is also given.
References
Maxwell Rosenlicht The American Mathematical Monthly, Vol. 79, No. 9. (Nov., 1972), pp. 963–972.
Кадець В. М. Курс функціонального аналізу та теорії міри. Львів: Серія «Університетська бібліотека», 2012. 590 с.
Trofymenko O. Convolution equations and mean value theorems for solutions of linear elliptic equations with constant coefficients in the complex plane. 2018. Journal of Mathematical Sciences. 2018. ol. 229, № 1. P. 96–107.
Гольберг А. А., Шеремета М. М., Заболоцький М. В., Скасків О. Б. Комплексний аналіз. Львів, 2020. 204 с.
Heyer H. The Liouville property for harmonic functions on groups and hypergroups. Methods of Functional Analysis and Topology. 2017. Vol. 23. N 1. P. 3–25.
Maxwell Alexander. Rosenlicht Liouville’s theorem on functions with elementary integrals. 1968. Vol. 24, No. 1. P.153–161.