On a filter for exponentially localized kernels based on Jacobi polynomials.

Let View the MathML source, and for k=0,1, View the MathML source denote the orthonormalized Jacobi polynomial of degree k. We discuss the construction of a matrix H so that there exist positive constants c, c1, depending only on H, α, and β such that View the MathML source Specializing to the case of Chebyshev polynomials, View the MathML source, we apply this theory to obtain a construction of an exponentially localized polynomial basis for the corresponding L2 space