Chopped Orthogonal Polynomial Expansions—Some Discrete Cases
Copyright policy )Chopped Orthogonal Polynomial Expansions—Some Discrete Cases
We study expansions of functions $f ( x )$ in terms of certain discrete families of orthogonal polynomials, $\{ p_i ( x ) \}$ where $x = 0,1, \cdots ,N,N$ finite or infinite. We assume f is known for $x\leqq M( M < N )$ and that the expansion in terms of the $p_i $’s is chopped after L terms $( L < N )$. This results in the need to study the eigenstructure of a certain “integral-type” operator. This eigenstructure is determined by producing a commuting second order difference operator.
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), simple spectrum, discrete, chopped orthogonal polynomial expansions, eigenfunctions, weight, finite convolution integral operator, second order differential operators
Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.), simple spectrum, discrete, chopped orthogonal polynomial expansions, eigenfunctions, weight, finite convolution integral operator, second order differential operators
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