Normal bivariate Birkhoff interpolation schemes and Pell equation
Marius Crainic; Nicolae Crainic
Commentationes Mathematicae Universitatis Carolinae (2009)
- Volume: 50, Issue: 2, page 265-272
- ISSN: 0010-2628
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topCrainic, Marius, and Crainic, Nicolae. "Normal bivariate Birkhoff interpolation schemes and Pell equation." Commentationes Mathematicae Universitatis Carolinae 50.2 (2009): 265-272. <http://eudml.org/doc/32497>.
@article{Crainic2009,
abstract = {Finding the normal Birkhoff interpolation schemes where the interpolation space and the set of derivatives both have a given regular “shape” often amounts to number-theoretic equations. In this paper we discuss the relevance of the Pell equation to the normality of bivariate schemes for different types of “shapes”. In particular, when looking at triangular shapes, we will see that the conjecture in Lorentz R.A., Multivariate Birkhoff Interpolation, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992, is not satisfied, and, at the same time, we will describe the complete solution.},
author = {Crainic, Marius, Crainic, Nicolae},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Birkhoff interpolation; Pell equation; Birkhoff interpolation; Pell equation; bivariate scheme},
language = {eng},
number = {2},
pages = {265-272},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Normal bivariate Birkhoff interpolation schemes and Pell equation},
url = {http://eudml.org/doc/32497},
volume = {50},
year = {2009},
}
TY - JOUR
AU - Crainic, Marius
AU - Crainic, Nicolae
TI - Normal bivariate Birkhoff interpolation schemes and Pell equation
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 2
SP - 265
EP - 272
AB - Finding the normal Birkhoff interpolation schemes where the interpolation space and the set of derivatives both have a given regular “shape” often amounts to number-theoretic equations. In this paper we discuss the relevance of the Pell equation to the normality of bivariate schemes for different types of “shapes”. In particular, when looking at triangular shapes, we will see that the conjecture in Lorentz R.A., Multivariate Birkhoff Interpolation, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992, is not satisfied, and, at the same time, we will describe the complete solution.
LA - eng
KW - Birkhoff interpolation; Pell equation; Birkhoff interpolation; Pell equation; bivariate scheme
UR - http://eudml.org/doc/32497
ER -
References
top- Barbeau E.J., Pell's Equation, Springer, New York, 2003. Zbl1030.11008MR1949691
- Lorentz R.A., Multivariate Birkhoff Interpolation, Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992. Zbl0760.41002MR1222648
- Gasca M., Maeztu J.I., 10.1007/BF01399308, Numer. Math. 39 (1982), 1--14. MR0664533DOI10.1007/BF01399308
- Stillwell J., Elements of number theory, Undergraduate Texts in Mathematics, Springer, New York, 2003. Zbl1112.11002MR1944957
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