Approximation properties of the $q$-sine bases

Details Approximation properties of the $q$-sine bases Approximation properties of the $q$-sine bases

2010-08-15

arxiv.org/abs/1008.2519v2

Mathematics

Spectral Theory

20 pages, 11 figures and 2 tables. We have fixed a number of typos and added references. Changed the title to better reflect t

Scientific paper

For $q>12/11$ the eigenfunctions of the non-linear eigenvalue problem associated to the one-dimensional $q$-Laplacian are known to form a Riesz basis of $L^2(0,1)$. We examine in this paper the approximation properties of this family of functions and its dual, in order to establish non-orthogonal spectral methods for the $p$-Poisson boundary value problem and its corresponding parabolic time evolution initial value problem. The principal objective of our analysis is the determination of optimal values of $q$ for which the best approximation is achieved for a given $p$ problem.

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