Convergence of the Schur algorithm

Author:
Olav Njåstad

Journal:
Proc. Amer. Math. Soc. **110** (1990), 1003-1007

MSC:
Primary 30B70; Secondary 40A15

DOI:
https://doi.org/10.1090/S0002-9939-1990-1028292-2

MathSciNet review:
1028292

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Abstract | References | Similar Articles | Additional Information

Abstract: Convergence of the Schur algorithm outside the unit circle is discussed with the aid of convergence theory for Schur continued fractions.

**[1]**W. B. Jones, O. Njåstad, and W. J. Thron,*Schur fractions, Perron-Carathéodory fractions and Szegő polynomials, a survey*, Analytic theory of continued fractions, II (Pitlochry/Aviemore, 1985) Lecture Notes in Math., vol. 1199, Springer, Berlin, 1986, pp. 127–158. MR**870247**, https://doi.org/10.1007/BFb0075938**[2]**William B. Jones, Olav Njåstad, and W. J. Thron,*Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle*, Bull. London Math. Soc.**21**(1989), no. 2, 113–152. MR**976057**, https://doi.org/10.1112/blms/21.2.113**[3]**William B. Jones and Wolfgang J. Thron,*Continued fractions*, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley Publishing Co., Reading, Mass., 1980. Analytic theory and applications; With a foreword by Felix E. Browder; With an introduction by Peter Henrici. MR**595864****[4]**Olav Njåstad,*A survey of some results on separate convergence of continued fractions*, Analytic theory of continued fractions, III (Redstone, CO, 1988) Lecture Notes in Math., vol. 1406, Springer, Berlin, 1989, pp. 88–115. MR**1034964**, https://doi.org/10.1007/BFb0096168**[5]**Hans-J. Runckel,*Bounded analytic functions in the unit disk and the behaviour of certain analytic continued fractions near the singular line*, J. Reine Angew. Math.**281**(1976), 97–125. MR**0393444**, https://doi.org/10.1515/crll.1976.281.97**[6]**I. Schur,*Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind*, J. Reine Angew. Math.**147**(1916), 205-232;**148**(1917), 122-145.**[7]**H. S. Wall,*Continued fractions and bounded analytic functions*, Bull. Amer. Math. Soc.**50**(1944), 110–119. MR**0010211**, https://doi.org/10.1090/S0002-9904-1944-08094-4

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1028292-2

Keywords:
Schur algorithm,
Schur continued fractions

Article copyright:
© Copyright 1990
American Mathematical Society