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References
Aczél, J.,Vorlesungen über Funktionalgleichungen und ihre Anwendungen (Berlin 1961).
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).
Fenyö, I.,Über eine Lösungsmethode gewisser Funktionalgleichungen, Acta Math. Acad. Sci. Hungar.7, 383–396 (1956).
Fenyö, I.,Über eine Funktionalgleichung, Math. Nachr.31, 103–109 (1966).
Fenyö, I.,Bemerkungen zur Funktionalgleichung f(x+y)+f(x−y)+af(x)=2g(x)h(y), Glasnik Mat.1 (21), 69–73 (1966).
Hörmander, L.,Linear Partial Differential Operators (Berlin−Göttingen−Heidelberg 1963).
Łojasiewicz, S.,Sur la fixation des variables dans une distribution, Studia Math.17, 1–64 (1958).
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).
Schwartz, L.,Théorie des distributions, I (Paris 1957).
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Światak, H. On the regularity of the distributional and continuous solutions of the functional\(\sum\limits_{i = 1}^k {ai(x,t)f(x + \varphi i(t))} = b(x,t)\) . Aeq. Math. 1, 6–19 (1968). https://doi.org/10.1007/BF01817554
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DOI: https://doi.org/10.1007/BF01817554