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2016 | 30 | 5--15
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On Popoviciu-Ionescu Functional Equation

Warianty tytułu
Języki publikacji
We study a functional equation first proposed by T. Popoviciu [15] in 1955. It was solved for the easiest case by Ionescu [9] in 1956 and, for the general case, by Ghiorcoiasiu and Roscau [7] and Radó [17] in 1962. Our solution is based on a generalization of Radó's theorem to distributions in a higher dimensional setting and, as far as we know, is different than existing solutions. Finally, we propose several related open problems.(original abstract)
Opis fizyczny
  • Universidad de Jaén, Spain
  • Aksoy A., Almira J.M., On Montel and Montel-Popoviciu theorems in several variables, Aequationes Math. 89 (2015), 1335-1357.
  • Almira J.M., Montel's theorem and subspaces of distributions which are Δ^m-invariant, Numer. Funct. Anal. Optim. 35 (2014), no. 4, 389-403.
  • Almira J.M., Abu-Helaiel K.F., On Montel's theorem in several variables, Carpathian J. Math. 31 (2015), 1-10.
  • Almira J.M., Székelyhidi L., Montel-type theorems for exponential polynomials, Demonstratio Math. 49 (2016), no. 2, 197-212.
  • Anselone P.M., Korevaar J., Translation invariant subspaces of finite dimension, Proc. Amer. Math. Soc. 15 (1964), 747-752.
  • Constantinescu F., La solution d'une équation fonctionnelle à l'aide de la théorie des distributions, Acta Math. Acad. Sci. Hungar. 16 (1965), 211-212.
  • Ghiorcoiasiu N., Roscau H., L'integration d'une équation fonctionnelle, Mathematica (Cluj) 4 (27) (1962), 21-32.
  • Hardy G.H., Wright E.M., An Introduction to the Theory of Numbers, Fifth edition, The Clarendon Press, Oxford University Press, New York, 1979.
  • Ionescu D.V., Sur une équation fonctionnelle, Studii si cercet. de mat. Cluj 8 (1956), 274-288.
  • Kuczma M., A survey of the theory of functional equations, Univ. Beograd. Publ. Elektrotchn. Fak. Ser. Mat. Fiz. 130 (1964), 1-64.
  • Levi-Civita T., Sulle funzioni che ammetono una formula d'addizione del tipo $f(x + y) = \sum_{i = 1}^n {X_i (x)Y_i (y)} $, R. C. Accad. Lincei 22 (1913), 181-183.
  • Montel P., Sur quelques extensions d'un théorème de Jacobi, Prace Matematyczno-Fizyczne 44 (1937), no. 1, 315-329.
  • Montel P., Sur quelques équations aux differences mêlées, Ann. Sci. École Norm. Sup. 65 (1948), no. 3, 337-353.
  • Montel P., Sur un système d'équations fonctionnelles, Ann. Soc. Polon. Math. 21 (1948), 99-106.
  • Popoviciu T., Sur quelques équations fonctionnelles, (Romanian) Acad. R. P. Romine. Fil. Cluj. Stud. Cerc. Sti. Ser. I 6 (1955), no. 3-4, 37-49.
  • Prager W., Schwaiger J., Generalized polynomials in one and several variables, Math. Pannon. 20 (2009), no. 2, 189-208.
  • Radó F., Caractérisation de l'ensemble des intégrales des équations différentielles linéaires homogènes à coefficients constants d'ordre donné, Mathematica (Cluj) 4 (27) (1962), 131-143.
  • Shulman E.V., Addition theorems and representations of topological semigroups, J. Math. Anal. Appl. 316 (2006), 9-15.
  • Shulman E.V., Decomposable functions and representations of topological semigroups, Aequationes Math. 79 (2010), no. 1-2, 13-21.
  • Shulman E.V., Some extensions of the Levi-Civita functional equation and richly periodic spaces of functions, Aequationes Math. 81 (2011), no. 1-2, 109-120.
  • Shulman E.V., Subadditive set-functions on semigroups, applications to group representations and functional equations, J. Funct. Anal. 263 (2012), no. 5, 1468-1484.
  • Shulman E.V., Subadditive maps and functional equations, Funct. Anal. Appl. 47 (2013), no. 4, 323-326.
  • Shulman E.V., Addition theorems and related geometric problems of the group representation theory, in: Recent Developments in Functional Equations and Inequalities, Banach Center Publ., Polish Acad. Sci. Inst. Math., Warsaw, 2013, pp. 155-172.
  • Stamate I., Contributii la integrarea unei ecuatii functionale, Inst. Politehn. Cluj, Lucrariti (1960), 47-51.
  • Stetkaer H., Functional equations on groups, World Scientific Publishing Co., Hackensack, 2013.
  • Székelyhidi L., Convolution type functional equations on topological abelian groups, World Scientific Publishing Co., Hackensack, 1991.
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