Geodesic
Difference equations having bases with powerlike growth which are perturbed by a~spectral parameter
Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 753-781

Voir la notice de l'article provenant de la source Math-Net.Ru

The asymptotic behaviour of solutions with powerlike growth of recurrence relations with a spectral parameter is investigated. A class of recurrence relations in which all basis solutions have powerlike growth is introduced. Recurrence relations in this class are linearly perturbed by a spectral parameter; for solutions of the new recurrence relations asymptotic formulae are obtained which are uniform with respect to the spectral parameter ranging within appropriate bounds. The theorems obtained are used for deriving new local asymptotic formulae for orthogonal and multiple orthogonal polynomials in a neighbourhood of the end-points of the support of the orthogonality weights. Bibliography: 14 titles.
Keywords: asymptotic behaviour of solutions of recurrence relations, local asymptotics of orthogonal and multiple orthogonal polynomials, Poincaré's theorem, Perron's theorem
Mots-clés : Birkhoff-Trjitzinsky theorem. 
@article{SM_2009_200_5_a6,
     author = {D. N. Tulyakov},
     title = {Difference equations having bases with powerlike growth which are perturbed by a~spectral parameter},
     journal = {Sbornik. Mathematics},
     pages = {753--781},
     publisher = {mathdoc},
     volume = {200},
     number = {5},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2009_200_5_a6/}
}
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D. N. Tulyakov. Difference equations having bases with powerlike growth which are perturbed by a~spectral parameter. Sbornik. Mathematics, Tome 200 (2009) no. 5, pp. 753-781. http://geodesic.mathdoc.fr/item/SM_2009_200_5_a6/