Gegenbauer Approximation in Certain Hilbert Spaces and Its Applications to Singular Differential Equations

Gegenbauer approximation in certain Hilbert spaces is investigated. Several weighted inverse inequalities and Poincare inequalities are obtained. Some approximation results are given. Singular differential equations are approximated by using Gegenbauer polynomials. This method keeps the spectral accuracy. The main idea and techniques used in this paper are also applicable to some singular problems in multiple-dimensional spaces.

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