Nontrivial solutions of linear functional equations: methods and examples

• Autorzy: Varga A. , Vincze C.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.6.957

• 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.

• University of Debrecen H-4010 Debrecen, P.O. Box 12 Hungary

autor

Vincze C.

• University of Debrecen H-4010 Debrecen, P.O. Box 12 Hungary

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.