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Algebraic structure of quasiradial solutions to the γ-harmonic equation
Volgograd State University, Russia.ORCID iD: 0000-0002-8422-6140
2006 (English)In: Pacific Journal of Mathematics, ISSN 0030-8730, E-ISSN 1945-5844, Vol. 226, no 1, 179-200 p.Article in journal (Refereed) Published
Abstract [en]

We obtain an explicit representation for quasiradial γ-harmonic functions, which shows that these functions have an essentially algebraic nature. We give a complete description of all γ that admit algebraic quasiradial solutions. Unlike the cases γ = ∞ and γ = 1, only finitely many algebraic solutions are shown to exist for any fixed |γ| > 1. A special extremal series of γ corresponds exactly to the well known ideal m-atomic gas adiabatic constant γ = (2m + 3)∕(2m + 1)..

Place, publisher, year, edition, pages
2006. Vol. 226, no 1, 179-200 p.
Keyword [en]
γ-harmonic function, quasiradial solution, algebraic function
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-79625DOI: 10.2140/pjm.2006.226.179OAI: oai:DiVA.org:liu-79625DiVA: diva2:607581
Available from: 2013-02-25 Created: 2012-08-11 Last updated: 2017-12-06

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Tkachev, Vladimir

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