Analytic Theory of Continued Fractions II Proceedings of a Seminar-W
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1199 Analytic Theory of Continued Fractions II Proceedings of a Seminar-Workshop held in Pitlochry and Aviemore, Scotland June 13-29, 1985
Edited by W.J. Thron
Spri nger-Verlag Berlin Heidelberg New York London Paris Tokyo
Editor
Wolfgang J. Thron Department of Mathematics, University of Colorado, Boulder Campus Box 426, Boulder, Colorado 80309, USA
Mathematics Subject Classification (1980): 30B70, 33A40, 65D99 ISBN 3-540-16768-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-16768-4 Springer-Verlag New York Heidelberg Berlin
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© Springer-Verlag Berlin Heidelberg 1986 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
PREFACE The success of the workshop held in Loen, Norway in the summer of 1981
(see Springer Lecture Notes in Mathematics No. 932) encouraged us
to arrange a second workshop in Pitlochry and Aviemore, Scotland in the summer of 1985. Waadeland.
Most of the organizational work was done by Haakon
Local arrangements were in the hands of John McCabe.
There were both continuity and progress in the topics treated at the two conferences. two subareas.
In these proceedings most contributions fall into
They are:
convergence theory of continued fractions and
continued fraction methods in the solution of strong moment problems. Under the first topic limit periodic continued fractions with or
receive most attention.
important role.
an
+
-1/4
Modified convergence also plays an
In the proofs element regions and value (limit) regions
are frequently used.
Many of the element regions are Cartesian ovals.
Truncation error estimates are obtained whenever feasible.
In the
second subarea Stieltjes, Hamburger and trigonometric moment problems are studied and various types of continued fractions, these problems, are investigated. to power series both at
0
useful in solving
These continued fractions correspond
and at
The two-point Pade tables, known
as M-tables are analyzed for some of these continued fractions.
Szego
polynomials coming up in connection with trigonometric moment problems are orthogonal on the unit circle.
In addition there are contributions
dealing with the location of the zeros of polynomials and multi-point Pade tables and applications to special functions.
Applicability of
results is emphasized in almost all articles. There is one survey article in this volume (pp. 127 - 158). other papers contain original research.
All
All contributions were refereed
and we appreciate the efforts of those who helped with this task. Grateful acknowledgement is made for the financial support of the Seminar
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