Chebyshev orthogonal polynomials and the Neumann problem |
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Authors: | M. N. Nebol’sina |
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Affiliation: | 1.Voronezh State University,Voronezh,Russia |
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Abstract: | In a Banach space E, we consider the Neumann problem for a second-order homogeneous equation with a constant operator coefficient densely defined in E. Under a weakened strong positivity condition on the operator coefficient (we use the approach due to V.I. Gorbachuk and A.I. Knyazyuk to the study of a-positive operators), we present a criterion for the well-posed solvability of the problem. We obtain a representation of the solution via Chebyshev operator polynomials of the first and second kind. |
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