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