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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-ba778873-143b-4c63-9f2c-e50299f62d0e

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Opuscula Mathematica

Tytuł artykułu

Nontrivial solutions of linear functional equations: methods and examples

Autorzy Varga, A.  Vincze, C. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN For a wide class of linear functional equations the solutions are generalized polynomials. The existence of non-trivial monomial terms of the solution strongly depends on the algebraic properties of some related families of parameters. As a continuation of the previous work [A. Varga, Cs. Vincze, G. Kiss, Algebraic methods for the solution of linear functional equations, Acta Math. Hungar.] we are going to present constructive algebraic methods of the solution in some special cases. Explicit examples will be also given.
Słowa kluczowe
EN linear functional equations   spectral analysis   field homomorphisms  
Wydawca AGH University of Science and Technology Press
Czasopismo Opuscula Mathematica
Rocznik 2015
Tom Vol. 35, no. 6
Strony 957--972
Opis fizyczny Bibliogr. 11 poz., wykr.
Twórcy
autor Varga, A.
autor Vincze, C.
Bibliografia
[1] Z. Daroczy, Notwendige und hinreichende Bedingungen fur die Existenz von nichtkon-stanten Losungen linearer Funktionalgleichungen, Acta Sci. Math. Szeged 22 (1961), 31-41.
[2] G. Kiss, A. Varga, Existence of nontrivial solutions of linear functional equations, Aequat. Math. 88 (2014), 151-162.
[3] M. Kuczma, An Introduction to the Theory of Functional Equations and Inequalities, Prace Naukowe Uniwersytetu Śląskiego w Katowicach, vol. CDLXXXIX, Państwowe Wydawnictwo Naukowe - Uniwersytet Śląski, Warszawa-Kraków-Katowice, 1985.
[4] M. Laczkovich, G. Kiss, Linear functional equations, differential operators and spectral synthesis, accepted for publication in Aequat. Math., published online 21 June 2014.
[5] M. Laczkovich, G. Kiss, Non-constant solutions of linear functional equations, 49th Int. Symp. on Functional equation, Graz (Austria), June 19-26, 2011, http://www.uni-graz.at/jens.schwaiger/ISFE49/talks/saturday/Laczkovich.pdf.
[6] L. Szekelyhidi, On a class of linear functional equations, Publ. Math. (Debrecen) 29 (1982), 19-28.
[7] L. Szekelyhidi, Convolution type functional equations on topological Abelian goups, World Scientific Publishing Co. Inc. Teaneck, NJ, 1991.
[8] A. Varga, On additive solutions of a linear equation, Acta Math. Hungar. 128 (2010), 15-25.
[9] A. Varga, Cs. Vincze, On Daróczy's problem, for additive functions, Publ. Math. (Debrecen) 75 (2009), 299-310.
[10] A. Varga, Cs. Vincze, On a functional equations containing weighted arithmetic means, International Series of Numerical Mathematics 157 (2009), 305-315.
[11] A. Varga, Cs. Vincze, G. Kiss, Algebraic methods for the solution of linear functional equations, accepted for publication in Acta Math. Hungar.
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-ba778873-143b-4c63-9f2c-e50299f62d0e
Identyfikatory
DOI http://dx.doi.Org/10.7494/OpMath.2015.35.6.957