A general functional equation
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- by J. H. B. Kemperman
- Trans. Amer. Math. Soc. 86 (1957), 28-56
- DOI: https://doi.org/10.1090/S0002-9947-1957-0094610-0
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References
- R. P. Boas Jr., Functions which are odd about several points, Nieuw Arch. Wisk. (3) 1 (1953), 27–32. MR 54836
- N. G. de Bruijn, Functions whose differences belong to a given class, Nieuw Arch. Wiskunde (2) 23 (1951), 194–218. MR 0043870
- N. G. de Bruijn, A difference property for Riemann integrable functions and for some similar classes of functions, Nederl. Akad. Wetensch. Proc. Ser. A. 55 = Indagationes Math. 14 (1952), 145–151. MR 0047120 T. Carleman, Les fonctions quasi-analytiques, Paris, 1926. H. Cramér, Random variables and probability distributions, Cambridge, 1937.
- Paul Erdös and Michael Golomb, Functions which are symmetric about several points, Nieuw Arch. Wisk. (3) 3 (1955), 13–19. MR 68723
- Hans Hahn, Über Funktionen mehrerer Veränderlicher, die nach jeder einzelnen Veränderlichen stetig sind, Math. Z. 4 (1919), no. 3-4, 306–313 (German). MR 1544367, DOI 10.1007/BF01203018
- H. Kestelman, On the functional equation $f(x+y)=f(x)+f(y)$, Fund. Math. 34 (1947), 144–147. MR 22298, DOI 10.4064/fm-34-1-144-147 J. F. Koksma, Diophantische Approximationen, Berlin, 1936. H. Lebesgue, Sur les fonctions représentables analytiquement, J. Math. Pures Appl. vol. 1 (1905) p. 201.
- Yu. V. Linnik, On some identically distributed statistics, Doklady Akad. Nauk SSSR (N.S.) 89 (1953), 9–11 (Russian). MR 0056223 J. Marcinkiewicz, Sur une propriété de la loi de Gauss, Math. Zeit. vol. 44 (1938) pp. 612-618. —, Sur les fonctions indépendantes III, Fund. Math. vol. 31 (1938) pp. 86-102. N. E. Nörlund, Differenzenrechnung, Berlin, 1924. A. Ostrowski, Über die Funktionalgleichung der Exponentialfunktion und verwante Funktionalgleichungen, Jber. Deutschen Math. Verein. vol. 38 (1929) pp. 54-62. S. Ruziewicz, Contribution à l’étude des ensembles de distances de points, Fund. Math. vol. 7 (1925) pp. 141-143. W. Sierpinsky, Démonstration élémentaire du théorème sur la densité des ensembles, Fund. Math. vol. 4 (1923) pp. 161-171. —, Hypothèse du continu, Warsaw, 1934, p. 135.
- V. P. Skitovič, Linear forms of independent random variables and the normal distribution law, Izv. Akad. Nauk SSSR Ser. Mat. 18 (1954), 185–200 (Russian). MR 0062972 H. Steinhaus, Sur les distances des points dans les ensembles de mesure positive, Fund. Math. vol. 1 (1920) pp. 93-104.
Bibliographic Information
- © Copyright 1957 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 86 (1957), 28-56
- MSC: Primary 39.00; Secondary 26.00
- DOI: https://doi.org/10.1090/S0002-9947-1957-0094610-0
- MathSciNet review: 0094610