On an orthogonal bivariate trigonometric Schauder basis for the space of continuous functions

What is it about?

In this paper we construct an orthogonal trigonometric Schauder basis in the space of continuous functions on the bivariate torus which has a small growth of the polynomial degree. The polynomial degree is considered in terms of the ℓ1- and ℓ∞-norm. To construct this basis we use a dyadic anisotropic periodic multiresolution analysis and corresponding wavelet spaces. The multiresolution analysis is formed using the sequence of only rotation matrices. The focus of attention is the estimation of the norm of the corresponding orthogonal projection operator.

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