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The Legendre-Type Polynomials and the Laguerre-Type Polynomials in a Sobolev Space

Allan M. Krall

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Abstract

We give only the highlights of these examples. That the polynomials are orthogonal is relatively easy, but showing that the differential operators, when restricted, remain self-adjoint is more difficult. We refer the interested reader to [3] and [4], for the details, which are quite complicated.

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What this paper is about

We give only the highlights of these examples. That the polynomials are orthogonal is relatively easy, but showing that the differential operators, when restricted, remain self-adjoint is more difficult. We refer the interested reader to [3] and [4], for the details, which are quite complicated.

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Available abstract

We give only the highlights of these examples. That the polynomials are orthogonal is relatively easy, but showing that the differential operators, when restricted, remain self-adjoint is more difficult. We refer the interested reader to [3] and [4], for the details, which are quite complicated.

Key concepts: Laguerre polynomials, Orthogonal polynomials, Classical orthogonal polynomials, Mathematics, Legendre polynomials, Type (biology), Jacobi polynomials, Sobolev space

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