Diagonal Padé approximants to hyperelliptic functions
Annales de la Faculté des sciences de Toulouse : Mathématiques (1996)
- Volume: S5, page 121-193
- ISSN: 0240-2963
Access Full Article
topHow to cite
topStahl, Herbert. "Diagonal Padé approximants to hyperelliptic functions." Annales de la Faculté des sciences de Toulouse : Mathématiques S5 (1996): 121-193. <http://eudml.org/doc/73401>.
@article{Stahl1996,
author = {Stahl, Herbert},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {rational approximation; Padé approximation; spurious poles; hyperelliptic functions; Baker-Gammel-Wills conjecture},
language = {eng},
pages = {121-193},
publisher = {Université Paul Sabatier, Institut de Mathématiques},
title = {Diagonal Padé approximants to hyperelliptic functions},
url = {http://eudml.org/doc/73401},
volume = {S5},
year = {1996},
}
TY - JOUR
AU - Stahl, Herbert
TI - Diagonal Padé approximants to hyperelliptic functions
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1996
PB - Université Paul Sabatier, Institut de Mathématiques
VL - S5
SP - 121
EP - 193
LA - eng
KW - rational approximation; Padé approximation; spurious poles; hyperelliptic functions; Baker-Gammel-Wills conjecture
UR - http://eudml.org/doc/73401
ER -
References
top- [BaGM] Baker ( G.A.) JR. and Graves-Morris . — Padé Approximants Parts I and Part II, Encycl. Math. Vols 13 and 14. Cambridge University Press, Cambridge (1981).
- [BGW] Baker ( G. A.) JR., Gammel ( J.L.) and Wills ( J.G.).- An investigation of the applicability of the Padé approximant method, J. Math. Anal. Appl.2 (1961), pp. 405-418. Zbl0102.05902MR130093
- [Br] Brezinsk I ( C.). — History of Continued Fractions and Padé approximants, Series in Comp. Math.12, Springer-Verlag, Heidelberg (1991). Zbl0714.01001MR1083352
- [Bo] Borchardt ( C.W.).— Application des transcendantes abéliennes á la théorie des fractions continues, J. Reine Angew. Math.48 (1854), pp. 69-104.
- [Ch] Chandrasehharan ( K.).— Analytic Number Theory, Springer-Verlag, Berlin ( 1968).
- [Du] Dumas ( S. ).— Sur le développement des fonctions elliptiques en fractions continues, Thésis, Univ. Zürich, (1908). Zbl39.0517.01JFM39.0517.01
- [Go] Gonchar ( A.A.).— A local condition for single-valuedness of analytic functions, Mat. Sbornik, 89 (131) (1972); English transl. in Math. USSR Sb.18 ( 1972), pp. 151-167. Zbl0257.30039MR322144
- [GoRa] Gonchar ( A.A.) and Rakhmanov ( E.A.).— Equilibrium distributions and degree of rational approximation of analytic functions , Mat. Sb.134 ( 1987); English transl. in Math. USSR Sb.62 ( 1989), pp. 305-48. Zbl0663.30039MR922628
- [Ham] Hamburger ( H.).— Über eine Erweiterung des Stieltjesschen Momentenproblems I, II, III, Math. Ann.81 (1920). pp. 235-319, Math. Ann.82 (1921), pp. 120-164, 168-187. Zbl47.0427.04JFM47.0427.04
- [Ha] Halphen ( G.-H. ).— Traité des fonctions elliptiques et de leurs applications, Tome II. Gauthier-Villars, Paris ( 1888). JFM20.0434.01
- [Hi] Hille ( E.). — Analytic Function Theory, Ginns and Company, Boston (1962). MR201608
- [HuCo] Hurwitz ( A. ) and Courant ( R.).— Funktionentheorie, Springer-Verlag, Berlin ( 1929).
- [Ja] Jacobi ( C.-G.-J. ).—Note sur une nouvelle application de l'analyse des functions elliptiques a l'algèbre, J. Reine Angew. Math.7 (1830), pp. 41-43.
- [Kr] Krein ( M.G. ). — The ideas of P. L. Chebychev and A. A. Markov in the theory of limiting values of integrals and their further development, Amer. Math. Soc. Transl. Series12 (1959), pp. 1-121. Zbl0087.04902MR113106
- [La] Landkof ( N.S. ).— Foundations of Modern Potential Theory , Springer-VerlagBerlin (1972). Zbl0253.31001MR350027
- [Lu] Lubinsky ( D.S.). - Divergence of complex rational approximants , Pacific J. Math.108 (1983), pp. 141-153. Zbl0476.30028MR709706
- [Nu1] Nuttall ( J.).— The convergence of Padé approximants of meromorphic functions, J. Math. Anal. Appl.31 (1970), pp. 129-140. Zbl0204.08602MR288279
- [Nu2] Nuttall ( J.).— Asymptotics of diagonal Hermite-Padé polynomials, J. Approx. Theory42 (1984), pp. 299-386. Zbl0565.41015MR769985
- [Pe] Perron ( O.). — Die Lehre von den Kettenbrüchen, Teubner, Stuttgard (1913).
- [Po1] POMMERENKE (CH.).— Ueber die Kapazitaet ebener Kontinuen , Math. Ann.139 ( 1959), pp. 64-75. Zbl0087.07002MR114922
- [Po2] Pommerenke ( CH. ).— Padé approximants and convergence in capacity, J. Math. Anal. Appl.41 (1973), pp. 775-780. Zbl0256.30037MR328090
- [Ra] Rakhmanov ( E.A.).— On the convergence of Padé approximants in classes of holomorphic functions, Math. USSR Sb.40 (1980), pp. 149-155. Zbl0466.30033
- [Si] Siegel ( C.L. ). - Transzendente Zahlen, Bibliographisches Institut, Mannheim ( 1967). Zbl0167.32202MR209231
- [Sp] Springer ( G. ). — Introduction to Riemann Surfaces , Chelsea publ. cop.New York (1981 ). Zbl0501.30039
- [St1] Stahl ( H. ).— Extremal domains associated with an analytic function I, II, Complex Variables Theory Appl.4 (1985), pp. 311-324, 325-338. Zbl0542.30027MR858916
- [St2] Stahl ( H. ).— The structure of extremal domains associated with an analytic function, Complex Variables Theory Appl.4 (1985), pp. 339-354. Zbl0542.30029MR858917
- [St3] Stahl ( H. ).— The convergence of Padé approximants to functions with branch points, Submitted to J. Approx. Theory. Zbl0896.41009MR1484040
- [Sti] Stieltjes ( T.-J.).— Recherches sur les fractions continues , Ann. Fac. Sci. Toulouse8 (1894), pp. 1-122. MR1508159JFM25.0326.01
- [StTo] Stahl ( H.) and Totik ( V.).- General Orthogonal Polynomials , Encycl. Math. Vol. 43, Cambridge University Press, Cambridge, (1992). Zbl0791.33009MR1163828
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.