Keywords
- Continue Fraction
- Projective Vector
- Admissible Sequence
- Extremal Polynomial
- Keldysh Inst
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
BERNSTEIN L., The Jacobi-Perron algorithm. Its theory and application., Lecture Notes in Mathematics, 207, Springer-Verlag, (1971).
GELFOND A.D., KUBENSKAYA I.M., On Perron theorem in the theory of finite-difference equations (in russian), Izv.Akad.Nauk SSSR, Ser.Mat., 17,83–86,(1953).
PARUSNIKOV V.I., The Jacobi-Perron algorithm and simultaneous approximation of functions (in russian), Mat. Sbornik, 114(156), 322–333,(1981).
PARUSNIKOV V.I., Limit-periodic multidimensional continued fractions (in russian), preprint, M.V. Keldysh Inst. of Appl. Math., Akad. Nauk SSSR, Moscow, No 62, (1983).
PERRON O., Gründlagen für eine Theorie des Jacobischen Kettenbruch Algorithmus., Math. Ann., 64,1–76, (1907).
PRINGSHEIM A., Über Konvergenz und functionen-theoretischen Character gewisser Limitar-periodische Kettenbrüche, Sitzungsber., Bayer. Akad. Wiss., München, Math.-Phys. 6, 1–52, (1910).
SCHWEIGER F., The Metrical Theory of Jacobi-Perron Algorithm., Lecture Notes in Mathematics, 334, Springer-Verlag, (1973).
SZÁSZ O., Über die Erhaltung der Konvergenz unendlicher Kettenbrüche bei independenter Veränderlichkeit aller ihrer Elemente, J. Reine Angew. Math., 147,(1917).
VAN VLECK E.B., On the convergence of algebraic continued fractions whose coefficients have limiting values, Trans. Am. Math. Soc., 5,253–262,(1904).
WIDOM H., Extremal polynomials assiociated with a system of curves in the complex plane, Adv.Math., 3,127–232,(1969).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
Parusnikov, V.I. (1987). On the convergence of the multidimensional limit-periodic continued fractions. In: Gilewicz, J., Pindor, M., Siemaszko, W. (eds) Rational Approximation and its Applications in Mathematics and Physics. Lecture Notes in Mathematics, vol 1237. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072466
Download citation
DOI: https://doi.org/10.1007/BFb0072466
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17212-3
Online ISBN: 978-3-540-47412-8
eBook Packages: Springer Book Archive
