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Approximation of analytic functions by rational functions with prescribed poles

1970; Wiley; Volume: 23; Issue: 3 Linguagem: Inglês

10.1002/cpa.3160230308

ISSN

1097-0312

Autores

Gaetano Fichera,

Tópico(s)

Approximation Theory and Sequence Spaces

Resumo

Communications on Pure and Applied MathematicsVolume 23, Issue 3 p. 359-370 Article Approximation of analytic functions by rational functions with prescribed poles Gaetano Fichera, Gaetano Fichera University of RomeSearch for more papers by this author Gaetano Fichera, Gaetano Fichera University of RomeSearch for more papers by this author First published: May 1970 https://doi.org/10.1002/cpa.3160230308Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Mergelyan, S. N., On the representation of functions by a series of polynomials on closed sets, Doklady Akad. Nauk SSSR N. S., Vol. 77, 1951, pp. 565–568. (In Russian.) Amer. Math. Soc. Transl., No. 3, 1962, pp. 287–293. 2 Mergelyan, S. N., Uniform approximation to functions of a complex variable, Uspekhi Mat. Nauk N. S., Vol. 7, No. 2(48), 1952, pp. 31–122. (In Russian.) Amer. Math. Soc. Transl., No. 3, 1962, pp. 294–391. 3 Weierstrass, K. T., Ueber die analytische Darstellbarkeit sogenannter willkürlicher Funktionen reeler Argumente, Sitzungsb. der K. Preuss. Akad. der Wiss. zu Berlin, 1885, pp. 633–639 and 789–805. 4 Runge, C., Zur Theorie der eindeutigen analytischen Funktionen, Acta Math., Vol. 6, 1885, pp. 228–244. 5 Runge, C., Entwicklung der Wurzeln einer algebraischen Gleichung in Summen von rationalen Funktionen der Koeffizienten, Acta Math., Vol. 6, 1885, pp. 205–318. 6 Walsh, J. L., On the expansion of analytic functions in series of polynomials, Trans. Amer. Math. Soc., Vol. 26, 1924, pp. 155–170. 7 Walsh, J. L., Ueber die Entwicklung einer analytischen Funktion nach Polynomen, Math, Ann., Vol. 96, 1926, pp. 430–436. 8 Walsh, J. L., Ueber die Entwicklung einer Funktion einer komplexen Veränderlichen nach Polynomen, Math. Ann., Vol. 96, 1926, pp. 437–450. 9 Hartogs, F., Ueber die Grenzfunktionen beschränkter Folgen von analytischen Funktionen, Math. Ann., Vol. 98, 1927, pp. 164–178. 10 Hartogs, F., and Rosenthal, A., Ueber Folgen analytischer Funktionen, Math. Ann., Vol. 100, 1928, pp. 212–263. 11 Hartogs, F., and Rosenthal, A., Ueber Folgen analytischer Funktionen, Math. Ann., Vol. 104, 1931, pp. 606–610. 12 Hilb, E., and Szàsz, O., Allgemeine Reihenentwicklungen, Enzyklopädie der Math. Wiss., Vol. 98, 1924, pp. 1129–1276. 13 Lavrentiev, M., On conformal mapping, Proc. Phys. Math. Inst. Steklov (Math. Sect.), Vol. 5, 1934, pp. 159–245. (In Russian.) 14 Lavrentiev, M., Sur les Fonctions d'une Variable Complexe Représentable par des Séries de Polynomes, Hermann et Cie., Paris, 1936. 15 Farrell, O. J., On approximation to a mapping function by polynomials, Amer. J. Math., Vol. 54, 1932, pp. 571–578. 16 Keldysh, M. V., Sur l'approximation des fonctions analytiques dans des domaines fermes, Mat. Sbornik N. S., Vol. 8, No. 50, 1940, pp. 137–148. 17 Keldysh, M. V., Sur la représentation par des series de polynomes des fonctions d'une variable complexe dans de domaines fermés, Mat. Sbornik N. S., Vol. 16, No. 58, 1945, pp. 249–258. 18 Hille, E., and Phillips, R. S., Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ., No. 31, 1957. 19 Kolmogorov, A. N., Sur les fonctions harmoniques conjuguées et les series de Fourier, Fund. Math., Vol. 7, 1925, pp. 23–28. 20 Hardy, G. H., Remarks on three recent notes in the Journal, J. London Math. Soc., Vol. 3, 1928, pp. 166–169. 21 Tamarkin, J. D., Remarks on the theory of conjugate functions, Proc. London Math. Soc., Vol. 34, 1932, pp. 379–391. 22 Zygmund, A., Trigonometrical Series, Vol. 1, 2nd Edit., Cambridge Univ. Press, 1959. 23 Fichera, G., Approssimazione uniforme delle funzioni olomorfe mediante funzioni razionali aventi poli semplici prefissati, I, II, Accad. Naz. Lincei, Rend. Classe Sci. Fis. Mat. Nat., Ser. 8, Vol. 27, 1959, pp. 193–201 and 317–323. 24 Fichera, G., Sull'approssimazione uniforme delle funzioni olomorfe con funzioni razionali aventi i poli prefissati, Accad. Naz. Lincei, Rend. Classe Sci. Fis. Mat. Nat., Ser. 8, Vol. 30, 1961, pp. 347–350. 25 Fichera, G., Sull'approssimazione delle funzioni olomorfe con funzioni razionali, Rend. Sem. Mat. Univ. Politec. Torino, Vol. 27, 1967–68, pp. 5–16. 26 De Vito, L., Sulle ipotesi di un teorema relativo alle funzioni olomorfe, Accad. Naz. Lincei, Rend. Classe Sci. Fis. Mat. Nat., Ser. 8, Vol. 43, 1967, pp. 453–463. Citing Literature Volume23, Issue3May 1970Pages 359-370 ReferencesRelatedInformation

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