Linear difference equations and exponential polynomials
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- by Walter Strodt PDF
- Trans. Amer. Math. Soc. 64 (1948), 439-466 Request permission
References
- S. Bochner, Hauptlösungen von Differenzengleichungen, Acta Math. 51 (1928), no. 1, 1–21 (German). MR 1555259, DOI 10.1007/BF02545658 É. Borel, Contribution a l’étude des fonctions méromorphes, Ann. École Norm. (3) vol. 18 (1901) pp. 211-239.
- R. D. Carmichael, Systems of linear difference equations and expansions in series of exponential functions, Trans. Amer. Math. Soc. 35 (1933), no. 1, 1–28. MR 1501670, DOI 10.1090/S0002-9947-1933-1501670-X
- Gustav Doetsch, Theorie und Anwendung der Laplace-Transformation, Dover Publications, New York, 1943 (German). MR 0009225
- M. Ghermanesco, Sur les équations aux différences finies, Acta Math. 62 (1933), no. 1, 239–287 (French). MR 1555385, DOI 10.1007/BF02393606 G. Halphén, Sur quelques séries pour le developpement des fonctions à une seule variable, Bull. Sci. Math. (2) vol. 5 (1881) pp. 462-488.
- R. E. Langer, On the zeros of exponential sums and integrals, Bull. Amer. Math. Soc. 37 (1931), no. 4, 213–239. MR 1562129, DOI 10.1090/S0002-9904-1931-05133-8 N. E. Nörlund, Vorlesungen über differenzenrechnung, Berlin, 1924.
- S. Pincherle, Sur la résolution de l’équation fonctionnelle $\sum h^v\phi (\alpha ^v)=f(x)$ à cofficients constantsà cofficients constants, Acta Math. 48 (1926), no. 3-4, 279–304 (French). MR 1555226, DOI 10.1007/BF02565335
- Rodolphe Raclis, Solution principale de l’équation linéaire aux différences finies, Acta Math. 55 (1930), no. 1, 277–394 (French). MR 1555318, DOI 10.1007/BF02546513
- I. M. Sheffer, A local solution of the difference equation $\Delta y(x)=F(x)$ and of related equations, Trans. Amer. Math. Soc. 39 (1936), no. 3, 345–379. MR 1501852, DOI 10.1090/S0002-9947-1936-1501852-X
- I. M. Sheffer, A correction: “A local solution of the difference equation $\Delta y(x)=F(x)$ and of related equations” [Trans. Amer. Math. Soc. 39 (1936), no. 3, 345–379; 1501852], Trans. Amer. Math. Soc. 41 (1937), no. 1, 153–159. MR 1501895, DOI 10.1090/S0002-9947-1937-1501895-7
- Walter Strodt, Analytic solutions of non-linear difference equations, Ann. of Math. (2) 44 (1943), 375–396. MR 11125, DOI 10.2307/1968969
- Walter Strodt, Principal solutions of difference equations, Amer. J. Math. 69 (1947), 717–757. MR 22990, DOI 10.2307/2371796 J. M. Whittaker, A theorem on meromorphic functions, Proc. London Math. Soc. (2) vol. 40 (1935-1936) pp. 255-272.
Additional Information
- © Copyright 1948 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 64 (1948), 439-466
- MSC: Primary 39.0X
- DOI: https://doi.org/10.1090/S0002-9947-1948-0027419-9
- MathSciNet review: 0027419