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Mat. Sb., 1994, Volume 185, Number 8, Pages 3–30 (Mi msb916)  

This article is cited in 50 scientific papers (total in 51 papers)

Asymptotic behavior of the $L^p$-norms and the entropy for general orthogonal polynomials

A. I. Aptekareva, V. S. Buyarovb, I. S. Degeza

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: The limit behavior of the sequence of $L^p$-norms of orthogonal polynomials is studied. Orthogonal polynomials on both a finite interval and the entire real line are considered. As a corollary, asymptotic formulas for entropy integrals containing orthogonal polynomials are obtained.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 373–395

Bibliographic databases:

UDC: 517.53
MSC: Primary 42C05; Secondary 42C99
Received: 20.12.1993

Citation: A. I. Aptekarev, V. S. Buyarov, I. S. Degeza, “Asymptotic behavior of the $L^p$-norms and the entropy for general orthogonal polynomials”, Mat. Sb., 185:8 (1994), 3–30; Russian Acad. Sci. Sb. Math., 82:2 (1995), 373–395

Citation in format AMSBIB
\by A.~I.~Aptekarev, V.~S.~Buyarov, I.~S.~Degeza
\paper Asymptotic behavior of the~$L^p$-norms and the~entropy for general orthogonal polynomials
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 8
\pages 3--30
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 373--395

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    This publication is cited in the following articles:
    1. Yanez R., Angulo J., Dehesa J., “Information Entropies of Many-Electron Systems”, Int. J. Quantum Chem., 56:5 (1995), 489–498  crossref  isi
    2. Aptekarev A., Buyarov V., WanAsche V., Deheza J., “Asymptotics of Entropy Integrals for Orthogonal Polynomials”, Dokl. Akad. Nauk, 346:4 (1996), 439–441  mathnet  mathscinet  zmath  isi
    3. Jorge Sánchez-Ruiz, “Logarithmic potential of Hermite polynomials and information entropies of the harmonic oscillator eigenstates”, J Math Phys (N Y ), 38:10 (1997), 5031  crossref  mathscinet  zmath  isi  elib
    4. Jorge Sánchez-Ruiz, “Asymptotic formula for the quantum entropy of position in energy eigenstates”, Physics Letters A, 226:1-2 (1997), 7  crossref  mathscinet  zmath  elib
    5. Buyarov V., “On Information Entropy for Gegenbauer Polynomials”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1997, no. 6, 8–11  mathscinet  zmath  isi
    6. Buyarov V., “On Distribution Function of Orthogonal Polynomial Values”, Vestn. Mosk. Univ. Seriya 1 Mat. Mekhanika, 1998, no. 4, 3–5  mathscinet  zmath  isi
    7. Dehesa J., Yanez R., Aptekarev A., Buyarov V., “Strong Asymptotics of Laguerre Polynomials and Information Entropies of Two-Dimensional Harmonic Oscillator and One-Dimensional Coulomb Potentials”, J. Math. Phys., 39:6 (1998), 3050–3060  crossref  mathscinet  zmath  adsnasa  isi
    8. Jorge S$aacute$nchez-Ruiz, J Phys A Math Gen, 32:18 (1999), 3419  crossref  mathscinet  zmath  isi
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    11. V S Buyarov, P López-Artés, A Martínez-Finkelshtein, W Van Assche, J Phys A Math Gen, 33:37 (2000), 6549  crossref  mathscinet  zmath  adsnasa  isi
    12. Lubinsky, DS, “Asymptotics of orthogonal polynomials: Some old, some new, some identities”, Acta Applicandae Mathematicae, 61:1–3 (2000), 207  crossref  mathscinet  zmath  isi  elib
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    35. J. S. Dehesa, A. Guerrero, P. Sánchez-Moreno, “Information-Theoretic-Based Spreading Measures of Orthogonal Polynomials”, Complex Anal. Oper. Theory, 2011  crossref  mathscinet
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    39. Bujar Xh. Fejzullahu, “On Orthogonal Expansions with Respect to the Generalized Jacobi Weight”, Results. Math, 2012  crossref  mathscinet
    40. B. Xh. Fejzullahu, F. Marcellán, J.J. Moreno-Balcázar, “Jacobi–Sobolev orthogonal polynomials: Asymptotics and a Cohen type inequality”, Journal of Approximation Theory, 2012  crossref  mathscinet  zmath
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