Geodesic
Orthogonality Relations for the Primitives of Legendre Polynomials and Their Applications to Some Spectral Problems for Differential Operators
Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 498-506

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In this paper, the properties of the primitives of Legendre polynomials on the interval $[0;1]$ are studied. It is proved that the Legendre polynomials form an “almost” orthogonal system. Namely, for a fixed order of the primitive, only finitely many of these polynomials can be nonorthogonal. These properties underly the relationship between the spectral problems for differential operators in $L_2[0;1]$ and the spectral properties of generalized Jacobi matrices.
Keywords: primitives of Legendre polynomials, least and greatest eigenvalue
Mots-clés : Jacobi matrix. 
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     author = {T. A. Garmanova and I. A. Sheipak},
     title = {Orthogonality {Relations} for the {Primitives} of {Legendre} {Polynomials} and {Their} {Applications} to {Some} {Spectral} {Problems} for {Differential} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
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T. A. Garmanova; I. A. Sheipak. Orthogonality Relations for the Primitives of Legendre Polynomials and Their Applications to Some Spectral Problems for Differential Operators. Matematičeskie zametki, Tome 110 (2021) no. 4, pp. 498-506. http://geodesic.mathdoc.fr/item/MZM_2021_110_4_a1/