Normal bivariate Birkhoff interpolation schemes and Pell equation
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 265-272
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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., {\it 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.
@article{CMUC_2009__50_2_a6,
author = {Crainic, Marius and Crainic, Nicolae},
title = {Normal bivariate {Birkhoff} interpolation schemes and {Pell} equation},
journal = {Commentationes Mathematicae Universitatis Carolinae},
pages = {265--272},
publisher = {mathdoc},
volume = {50},
number = {2},
year = {2009},
mrnumber = {2537835},
zbl = {1212.65040},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2009__50_2_a6/}
}
TY - JOUR AU - Crainic, Marius AU - Crainic, Nicolae TI - Normal bivariate Birkhoff interpolation schemes and Pell equation JO - Commentationes Mathematicae Universitatis Carolinae PY - 2009 SP - 265 EP - 272 VL - 50 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/CMUC_2009__50_2_a6/ LA - en ID - CMUC_2009__50_2_a6 ER -
%0 Journal Article %A Crainic, Marius %A Crainic, Nicolae %T Normal bivariate Birkhoff interpolation schemes and Pell equation %J Commentationes Mathematicae Universitatis Carolinae %D 2009 %P 265-272 %V 50 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/CMUC_2009__50_2_a6/ %G en %F CMUC_2009__50_2_a6
Crainic, Marius; Crainic, Nicolae. Normal bivariate Birkhoff interpolation schemes and Pell equation. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 265-272. http://geodesic.mathdoc.fr/item/CMUC_2009__50_2_a6/