@article{SM_1995_82_2_a8,
author = {A. I. Aptekarev and V. S. Buyarov and I. S. Degeza},
title = {Asymptotic behavior of the~$L^p$-norms and the~entropy for general orthogonal polynomials},
journal = {Sbornik. Mathematics},
pages = {373--395},
year = {1995},
volume = {82},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1995_82_2_a8/}
}
TY - JOUR AU - A. I. Aptekarev AU - V. S. Buyarov AU - I. S. Degeza TI - Asymptotic behavior of the $L^p$-norms and the entropy for general orthogonal polynomials JO - Sbornik. Mathematics PY - 1995 SP - 373 EP - 395 VL - 82 IS - 2 UR - http://geodesic.mathdoc.fr/item/SM_1995_82_2_a8/ LA - en ID - SM_1995_82_2_a8 ER -
A. I. Aptekarev; V. S. Buyarov; I. S. Degeza. Asymptotic behavior of the $L^p$-norms and the entropy for general orthogonal polynomials. Sbornik. Mathematics, Tome 82 (1995) no. 2, pp. 373-395. http://geodesic.mathdoc.fr/item/SM_1995_82_2_a8/
[1] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR
[2] Angulo J. C., Dehesa J. S., “Tight rigorus bounds to atomic information entropies”, J. Chem. Phys., 97(9) (1992), 6485–6495 | DOI
[3] Aptekarev A. I., “Asimptotika ortogonalnykh mnogochlenov v okrestnosti kontsov intervala ortogonalnosti”, Matem. sb., 183:5 (1992), 43–62 | MR
[4] Babenko K. I., “Ob odnom neravenstve v teorii integrala Fure”, Izv. AN SSSR. Seriya matem., 25 (1961), 531–542 | MR | Zbl
[5] Bari N. K., Trigonometricheskie ryady, GIFML, M., 1961 | MR
[6] Bernshtein S. N., Sobranie sochinenii, T. 2, Izdatelstvo AN SSSR, M., 1954
[7] Bialynicki-Birula I., Mycielski J., “Uncertainty Relations for Information Entropy in Wave Mechanics”, Commun. Math. Phys., 44 (1975), 129–132 | DOI | MR
[8] Buyarov V. S., “O logarifmicheskoi asimptotike dlya polinomov, ortogonalnykh na $\mathbb R$ s nesimmetricheskimi vesami”, Mat. zametki, 50:2 (1991), 28–36 | MR | Zbl
[9] Geronimus Ya. L., Mnogochleny ortogonalnye na okruzhnosti i na otrezke, GIFML, M., 1958
[10] Kalyaguine V. A., “On asymptotics of $L_p$ extremal polynomials on a complex curve”, J. Appr. Theory, 74 (1993), 226–236 | DOI | MR
[11] Kusis P., Vvedenie v teoriyu prostranstv $H^p$, Mir, M., 1984 | MR
[12] Lubinsky D. S. and Saff E. B., Strong asymptotics for $L_p$ extremal polynomials $(1
\leq \infty )$ associated with weights on $[-1,1]$, Preprint ICM #87-011 | MR | Zbl[13] Lubinsky D. S., Saff E. B., Strong asymptotics for Extremal Polynomials associated with Weights on $\mathbb R$, Lect. Notes in Math., 1305, Springer, Berlin, 1987 | MR
[14] Rakhmanov E. A., “O gipoteze V.A. Steklova v teorii ortogonalnykh mnogochlenov”, Matem. sb., 108(150) (1979), 581–608 | MR | Zbl
[15] Rakhmanov E. A., “Strong asymptotics for orthogonal polynomials”, Methods of Approximation Theory in Complex Analysis and Mathematical Physics, eds. Gonchar A. A., Saff E. B., Nauka, M., 1992, 71–97 | MR
[16] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962
[17] Suetin P. K., “Problema V.A. Steklova v teorii ortogonalnykh mnogochlenov”, Itogi nauki i tekhniki. Matem. analiz, 15, 1977, 5–82 | MR | Zbl
[18] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1967 | MR