**Jürgen Prestin, Frauke Sprengel**

**An Orthonormal Bivariate Algebraic Polynomial Basis for $C(I^2)$ of Low Degree**

**The paper is published:**
Multivariate Approximation: Recent Trends and Results (Eds. W. Haußmann, K. Jetter, M. Reimer) Mathematical Research, Vol. 101, Akademie-Verlag, Berlin 1997, 177-188

**MSC:**- 41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}
- 42B99 None of the above but in this section

**Abstract:** For any fixed $\epsilon>0$, we construct an orthonormal Schauder

basis $\{P_\mu\}_{\mu=0}^\infty$ for $C(I^2)$ consisting of

bivariate algebraic polynomials $P_\mu$ with $(deg_q P_\mu)^2
as a generalization of the corresponding univariate basis constructed

in [1]. The orthogonality is with respect to the bivariate Chebyshev

weight.

**Keywords:** *Schauder basis, polynomial wavelet packets, Chebyshev polynomials*