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aequationes mathematicae

, Volume 1, Issue 1–2, pp 6–19 | Cite as

On the regularity of the distributional and continuous solutions of the functional\(\sum\limits_{i = 1}^k {ai(x,t)f(x + \varphi i(t))} = b(x,t)\)

  • Halina Światak
Research Papers

Keywords

Continuous Solution 
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References

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    Aczél, J.,Vorlesungen über Funktionalgleichungen und ihre Anwendungen (Berlin 1961).Google Scholar
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    Aczél, J., Haruki, H., McKiernan, M. A., andSakovič, G. N.,General and Regular Solutions of Functional Equations Characterizing Harmonic Polynomials, Aequationes Math.1, 37–53 (1968).Google Scholar
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    Fenyö, I.,Über eine Lösungsmethode gewisser Funktionalgleichungen, Acta Math. Acad. Sci. Hungar.7, 383–396 (1956).Google Scholar
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    Fenyö, I.,Über eine Funktionalgleichung, Math. Nachr.31, 103–109 (1966).Google Scholar
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    Fenyö, I.,Bemerkungen zur Funktionalgleichung f(x+y)+f(x−y)+af(x)=2g(x)h(y), Glasnik Mat.1 (21), 69–73 (1966).Google Scholar
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    Hörmander, L.,Linear Partial Differential Operators (Berlin−Göttingen−Heidelberg 1963).Google Scholar
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    Łojasiewicz, S.,Sur la fixation des variables dans une distribution, Studia Math.17, 1–64 (1958).Google Scholar
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    Światak, H.,On the Regularity of the Locally Integrable Solutions of the Functional Equations \(\sum\limits_{i = 1}^k {ai(x,t)f(x + \varphi i(t))} = 0\), Publ. Math. Debrecen (to appear).Google Scholar
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    Schwartz, L.,Théorie des distributions, I (Paris 1957).Google Scholar

Copyright information

© Birkhäuser-Verlag 1968

Authors and Affiliations

  • Halina Światak
    • 1
  1. 1.Jagello UniversityCracowPoland

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