| Title:
|
Normal bivariate Birkhoff interpolation schemes and Pell equation (English) |
| Author:
|
Crainic, Marius |
| Author:
|
Crainic, Nicolae |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
265-272 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Birkhoff interpolation |
| Keyword:
|
Pell equation |
| MSC:
|
11D09 |
| MSC:
|
65D05 |
| idZBL:
|
Zbl 1212.65040 |
| idMR:
|
MR2537835 |
| . |
| Date available:
|
2009-08-18T12:25:01Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133432 |
| . |
| Reference:
|
[1] Barbeau E.J.: Pell's Equation.Springer, New York, 2003. Zbl 1030.11008, MR 1949691 |
| Reference:
|
[2] Lorentz R.A.: Multivariate Birkhoff Interpolation.Lecture Notes in Mathematics, 1516, Springer, Berlin-Heidelberg, 1992. Zbl 0760.41002, MR 1222648 |
| Reference:
|
[3] Gasca M., Maeztu J.I.: On Lagrange and Hermite interpolation in $\mathbb R^n$.Numer. Math. 39 (1982), 1--14. MR 0664533, 10.1007/BF01399308 |
| Reference:
|
[4] Stillwell J.: Elements of number theory.Undergraduate Texts in Mathematics, Springer, New York, 2003. Zbl 1112.11002, MR 1944957 |
| . |
