Solutions of algebraic equations with the
analytic almost periodic coefficients (in Russian)

V. V. Britik

We prove that continuous solutions of algebraic equations with the holomorphic in a tube domain almost periodic coefficients are almost periodic in this domain too.

1. Cameron R. H. Implicit functions of almost periodic functions // Bull. Amer. Math. Soc. – 1934. – V.40. – P.895–904.

2. Bohr H., Flanders D. A. Algebraic equation with almost-periodic coefficients // Mat.-fysike Medd. – 1937. – № 15. – P.1–49.

3. Walther A. Algebraische Funktionen von fastperiodischen Funktionen // Monatshefte für Mathematik und Physik. – 1933. – № 40. – P.444–457.

4. Bohr H., Flanders D. A. Algebraic functions of almost-periodic functions// Duke Math. J. – 1938. – № 4. – P.779–787.

5. Левитан Б. М. Почти-периодические функции. – Москва: ГИТТЛ., 1953. – 396 с.

6. Jessen B., Torneave H. Mean motion and zeros of almost-periodic functions // Acta Math. – 1945. – P.137–279.

7. Brytik V. V., Favorov S. Yu. Solution of algebraic equations with almost-periodic coefficients // МАГ. – 2000. – № 4.

8. Бор Г. Почти периодические функции. – Москва-Ленинград, ОГИЗ., 1934. – 128 с.

9. Ронкин Л.И., Теоремы Иессена для голоморфных почти периодических функций в трубчатых областях // Сиб. мат. журн. – 1987. –Т.28, № 3. – C.199–204.

	Solutions of algebraic equations with the analytic almost periodic coefficients (in Russian)
Author	V. V. Britik vladimir@valbri.kharkov.ua V. N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv 61077, Ukraine
Abstract	We prove that continuous solutions of algebraic equations with the holomorphic in a tube domain almost periodic coefficients are almost periodic in this domain too.
Keywords	continuous solutions of algebraic equations, holomorphic in a tube domain almost periodic coefficients, almost periodic in this domain
DOI	doi:10.30970/ms.15.2.191-199
Reference	1. Cameron R. H. Implicit functions of almost periodic functions // Bull. Amer. Math. Soc. – 1934. – V.40. – P.895–904. 2. Bohr H., Flanders D. A. Algebraic equation with almost-periodic coefficients // Mat.-fysike Medd. – 1937. – № 15. – P.1–49. 3. Walther A. Algebraische Funktionen von fastperiodischen Funktionen // Monatshefte für Mathematik und Physik. – 1933. – № 40. – P.444–457. 4. Bohr H., Flanders D. A. Algebraic functions of almost-periodic functions// Duke Math. J. – 1938. – № 4. – P.779–787. 5. Левитан Б. М. Почти-периодические функции. – Москва: ГИТТЛ., 1953. – 396 с. 6. Jessen B., Torneave H. Mean motion and zeros of almost-periodic functions // Acta Math. – 1945. – P.137–279. 7. Brytik V. V., Favorov S. Yu. Solution of algebraic equations with almost-periodic coefficients // МАГ. – 2000. – № 4. 8. Бор Г. Почти периодические функции. – Москва-Ленинград, ОГИЗ., 1934. – 128 с. 9. Ронкин Л.И., Теоремы Иессена для голоморфных почти периодических функций в трубчатых областях // Сиб. мат. журн. – 1987. –Т.28, № 3. – C.199–204.
Pages	191-199
Volume	15
Issue	2
Year	2001
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Solutions of algebraic equations with the analytic almost periodic coefficients (in Russian)