Multiplicatively periodic subharmonic functions in the punctured Euclidean space |
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| Author |
kond@franko.lviv.ua, vasylyna1992@rambler.ru
Lviv National University
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| Abstract |
It is proved that each multiplicatively periodic subharmonic
function in $\mathbb{R}^m\backslash\{0 \}$, $m\geq3$, is constant.
Examples of non-constant multiplicatively periodic
differences of subharmonic in $\mathbb{R}^m\backslash\{0 \}$ functions are constructed.
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| Keywords |
subharmonic function; multiplicatively periodic function; Riesz measure; distribution function of a measure
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| Reference |
1. O. Rausenberger, Lehrbuch der Theorie der periodischen Funktionen einer Variabeln, Leipzig, Druck und
Ferlag von B.G.Teubner, 1884, 470 p.
2. Y. Hellegouarch, Invitation to the Mathematics of Fermat-Wiles, Academic Press, 2002, 381 p. 3. G. Valiron, Cours d’Analyse Mathematique, Theorie des fonctions, 2nd Edition, Masson et.Cie., Paris, 1947, 522 p. 4. O.P. Gnatiuk, A.A. Kondratyuk, Subharmonic functions and electric fields in ball layers. I, Mat. Stud., 34 (2010), ¹2, 180–192. 5. O. Gnatiuk, A. Kondratyuk, Yu. Kudjavina, Classification of isolated singularities of subharmonic functions, Visnyk Lviv. Univ., Ser. Mech. Math., 74 (2011), 52–60. 6. W.K. Hayman, P.B. Kennedy, Subharmonic functions, V.1, Academic Press, London, New York, San Francisco, 1976. 7. F. Schottky, Uber eine specielle Funktion welche bei einer bestimmten linearen Transformation ihres Arguments unverandert bleibt, J. Reine Angew. Math., 101 (1887), 227–272. 8. F. Klein, Zur Theorie der Abel’schen Funktionen, Math. Ann., 36 (1890), 1–83. 9. D.G. Crowdy, Geometric function theory: a modern view of a classical subject, IOP Publishing Ltd and London Mathematical Society, Nonlinearity, 21 (2008), 205–219. |
| Pages |
159-164
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| Volume |
40
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| Issue |
2
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| Year |
2013
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |