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Positive multipoint Padé continued fractions

Published online by Cambridge University Press:  20 January 2009

Erik Hendriksen  and
Olav Njåstad
Erik Hendriksen
Affiliation:
Department of Mathematics, University of Amsterdam, Roetersstraat 15, 1018 WB Amsterdam, The Netherlands
Olav Njåstad
Affiliation:
Department of Mathematics, University of Trondheim-NTH, N-7034 Trondheim, Norway
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Multipoint Padé fractions were introduced in [2]. They are continued fractions defined in the following way:

Let {a1,a2,…,ap} be given fixed points in the complex plane. For each n ≧1 let an = am where 1≦m≦p and n≡m (mod p).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 32 , Issue 2 , June 1989 , pp. 261 - 269
Copyright
Copyright © Edinburgh Mathematical Society 1989

References

REFERENCES

1.Akhiezer, N. I., The Classical Moment Problem and Some Related Questions in Analysis (Hafner Publishing Company, New York 1965).Google Scholar
2.Hendriksen, E. and Njåstad, O., A Favard theorem for rational functions, J. Math. Anul. Appl., to appear.Google Scholar
3.Jones, W. B., Njåstad, O. and Thron, W. J., Continued fractions and strong Hamburger moment problems, Proc. London Math Soc. (3) 47 (1983), 363–384.CrossRefGoogle Scholar
4.Jones, W. B. and Thron, W. J., Continued Fractions: Analytic Theory and Applications (Addison-Wesley Publ. Co., Reading, MA 1980).Google Scholar
5.Jones, W. B. and Thron, W. J., Survey of continued fractions methods of solving moment problems and related topics, Analytic Theory of Continued Fractions (Eds. Jones, W. B., Thron, W. J. and Waadeland, H., Springer Lecture Notes in Mathematics 932, Berlin (1982), 4–37.CrossRefGoogle Scholar
6.Landau, H. J., The classical moment problem: Hilbertian proofs, J. Funct. Anal. 38 (1980), 255–272.CrossRefGoogle Scholar
7.Njåstad, O., An extended Hamburger moment problem, Proc. Edinburgh Math. Soc. (Series II) 28 (1985), 167–183.CrossRefGoogle Scholar
8.Njåstad, O., Unique solvability of an extended Hamburger moment problem, J. Math. Anal. Appl. 124 (1987), 502–519.CrossRefGoogle Scholar
9.Njåstad, O., Multipoint Padé approximation and orthogonal rational functions, Nonlinear Numerical Methods and Rational Approximation (Ed.: Cuyt, A., Reidel Publ. Co. 1988), 259–270.CrossRefGoogle Scholar
10.Njåstad, O., Contractive Laurent fractions and nested discs, J. Approx. Theory, to appear.Google Scholar
11.Njåstad, O., and Thron, W. J., Rational functions and quadrature formulae, Analysis, to appear.Google Scholar
12.Perron, O., Die Lehre von den Kettenbrüchen, 3. Auflage, Band 2 (Teubner, Stuttgart 1957).Google Scholar
13.Shohat, J. A. and Tamarkin, J. D., The Problem of Moments (Mathematical Surveys No. 1, Amer. Math. Soc., Providence, RI 1943).CrossRefGoogle Scholar