Approximation properties of the $q$-sine bases

Abstract

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.

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

Cited by in corpus (3)

• The basis property of generalized Jacobian elliptic functions
• Basis properties of the p,q-sine functions
• Remarkable properties of the ${\text{sinc}}_{p,q}$ functions and related integrals