On similarity of some
Pommier operators in spaces of analytic functions (in Ukrainian)

M.I. Nahnybida; Ya.V. Mykytyuk

Let $A_R$, ($0 < R\le \infty$) be the space of all analytic in disk $|\zeta| < R$ functions, with usual topology, $(\Delta f)(\zeta)=\frac{f(\zeta)-f(0)}{\zeta} $ the Pommier operator in this space. The necessary and sufficient conditions of similarity of the operators $L_0 =z^j\Delta ^{m+s} $ and $L=\sum_{j=0}^s\alpha_{s-j}z^s\Delta ^{m+j} $, where $m,s \in \Bbb N $ and $\alpha_j$ ($j=0,1,\dots,s $) are fixed functions from $A_R$ are obtained.

1. Köthe G. Dualität in der Funktionentheorie J. für Reine und Angew. Math. – 1953. – Bd.191. – S.30–49.

2. Нагнибіда М.І. Класичні оператори в просторах аналітичних функцій. – Київ: Інститут математики НАН України, 1995. – 297с.

3. Фаге М.К., Нагнибида Н.И. Проблема эквивалентности обыкновенных линейных диференциальных операторов. – Новосибирск: Наука, 1987. – 280с.

4. Коллингвуд Э., Ловатер А. Теория предельных множеств. – Москва: Мир, 1971. – 312с.

	On similarity of some Pommier operators in spaces of analytic functions (in Ukrainian)
Author	M.I. Nahnybida, Ya.V. Mykytyuk Yuriy Fedkovych Chernivtsi National University, 2 Kotsiubynskoho St., Chernivtsi 274012, Ukraine, Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, 1 Universytetska St., Lviv 290602, Ukraine
Abstract	Let $A_R$, ($0 < R\le \infty$) be the space of all analytic in disk $\|\zeta\| < R$ functions, with usual topology, $(\Delta f)(\zeta)=\frac{f(\zeta)-f(0)}{\zeta} $ the Pommier operator in this space. The necessary and sufficient conditions of similarity of the operators $L_0 =z^j\Delta ^{m+s} $ and $L=\sum_{j=0}^s\alpha_{s-j}z^s\Delta ^{m+j} $, where $m,s \in \Bbb N $ and $\alpha_j$ ($j=0,1,\dots,s $) are fixed functions from $A_R$ are obtained.
Keywords	analytic functions in disk, Pommier operator, similarity of operators
DOI	doi:10.30970/ms.9.2.193-198
Reference	1. Köthe G. Dualität in der Funktionentheorie J. für Reine und Angew. Math. – 1953. – Bd.191. – S.30–49. 2. Нагнибіда М.І. Класичні оператори в просторах аналітичних функцій. – Київ: Інститут математики НАН України, 1995. – 297с. 3. Фаге М.К., Нагнибида Н.И. Проблема эквивалентности обыкновенных линейных диференциальных операторов. – Новосибирск: Наука, 1987. – 280с. 4. Коллингвуд Э., Ловатер А. Теория предельных множеств. – Москва: Мир, 1971. – 312с.
Pages	193-198
Volume	9
Issue	2
Year	1998
Journal	Matematychni Studii
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Table of content of issue	html

On similarity of some Pommier operators in spaces of analytic functions (in Ukrainian)