메뉴 건너뛰기




Volumn 125, Issue 2, 2003, Pages 198-237

Strong asymptotics of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight

Author keywords

Bessel functions; Generalized Jacobi weight; Riemann Hilbert problems; Steepest descent method

Indexed keywords


EID: 0348222398     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jat.2003.11.005     Document Type: Article
Times cited : (48)

References (21)
  • 2
    • 0000787499 scopus 로고
    • Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval
    • V.M. Badkov, Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval, Math. USSR, Sbornik 24 (1974) 223-256.
    • (1974) Math. USSR, Sbornik , vol.24 , pp. 223-256
    • Badkov, V.M.1
  • 3
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • (1)
    • P. Bleher, A. Its, Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model, Ann. of Math. (2) 150 (1) (1999) 185-266.
    • (1999) Ann. of Math. , vol.150 , Issue.2 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 5
    • 0003346458 scopus 로고    scopus 로고
    • Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
    • Courant Institute of Mathematical Sciences, New York University
    • P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics Vol. 3, Courant Institute of Mathematical Sciences, New York University, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.3
    • Deift, P.1
  • 6
    • 0033440723 scopus 로고    scopus 로고
    • Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
    • P. Deift, T. Kriecherbauer, K.T.-R. McLaughlin, S. Venakides, X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Commun. Pure Appl. Math. 52 (11) (1999) 1335-1425.
    • (1999) Commun. Pure Appl. Math. , vol.52 , Issue.11 , pp. 1335-1425
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 9
    • 0001525213 scopus 로고
    • A steepest descent method for oscillatory Riemann-Hilbert problems, Asymptotics for the MKdV equation
    • (2)
    • P. Deift, X. Zhou, A steepest descent method for oscillatory Riemann-Hilbert problems, Asymptotics for the MKdV equation, Ann. of Math. (2) 137 (2) (1993) 295-368.
    • (1993) Ann. of Math. , vol.137 , Issue.2 , pp. 295-368
    • Deift, P.1    Zhou, X.2
  • 10
    • 21344498327 scopus 로고
    • Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials
    • T. Erdélyi, P. Nevai, A.P. Magnus, Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (2) (1994) 602-614.
    • (1994) SIAM J. Math. Anal. , vol.25 , Issue.2 , pp. 602-614
    • Erdélyi, T.1    Nevai, P.2    Magnus, A.P.3
  • 11
    • 0001283085 scopus 로고
    • The isomonodromy approach to matrix models in 2D quantum gravity
    • A.S. Fokas, A.R. Its, A.V. Kitaev, The isomonodromy approach to matrix models in 2D quantum gravity, Commun. Math. Phys. 147 (2) (1992) 395-430.
    • (1992) Commun. Math. Phys. , vol.147 , Issue.2 , pp. 395-430
    • Fokas, A.S.1    Its, A.R.2    Kitaev, A.V.3
  • 12
    • 0003411407 scopus 로고
    • 2nd Edition, Dover Publications, New York
    • F.D. Gakhov, Boundary Value Problems, 2nd Edition, Dover Publications, New York, 1990.
    • (1990) Boundary Value Problems
    • Gakhov, F.D.1
  • 13
    • 38149147215 scopus 로고
    • Reflection coefficients for the generalized Jacobi weight functions
    • L.B. Golinskii, Reflection coefficients for the generalized Jacobi weight functions, J. Approx. Theory 87 (1) (1994) 117-126.
    • (1994) J. Approx. Theory , vol.87 , Issue.1 , pp. 117-126
    • Golinskii, L.B.1
  • 14
    • 0345982308 scopus 로고    scopus 로고
    • Strong asymptotics of polynomials orthogonal with respect to Freud weights
    • T. Kriecherbauer, K.T.-R. McLaughlin, Strong asymptotics of polynomials orthogonal with respect to Freud weights, Internat. Math. Res. Not. 1999 (6) (1999) 299-333.
    • (1999) Internat. Math. Res. Not. 1999 , Issue.6 , pp. 299-333
    • Kriecherbauer, T.1    McLaughlin, K.T.-R.2
  • 15
    • 0344509264 scopus 로고    scopus 로고
    • Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter
    • A.B.J. Kuijlaars, K.T.-R. McLaughlin, Riemann-Hilbert analysis for Laguerre polynomials with large negative parameter, Comput. Methods Function Theory 1 (1) (2001) 205-233.
    • (2001) Comput. Methods Function Theory , vol.1 , Issue.1 , pp. 205-233
    • Kuijlaars, A.B.J.1    McLaughlin, K.T.-R.2
  • 16
    • 0003626550 scopus 로고    scopus 로고
    • The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials
    • Preprint, to appear in Adv. Math
    • A.B.J. Kuijlaars, K.T.-R. McLaughlin, W. Van Assche, M. Vanlessen, The Riemann-Hilbert approach to strong asymptotics for orthogonal polynomials, Preprint, 2001, http://xxx.lanl.gov/abs/math.CA/0111252, to appear in Adv. Math.
    • (2001)
    • Kuijlaars, A.B.J.1    McLaughlin, K.T.-R.2    Van Assche, W.3    Vanlessen, M.4
  • 17
    • 0038984584 scopus 로고
    • Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equation: Numerical explorations
    • A.P. Magnus, Asymptotics for the simplest generalized Jacobi polynomials recurrence coefficients from Freud's equation: numerical explorations, Ann. Numer. Math. 2 (1-4) (1995) 311-325.
    • (1995) Ann. Numer. Math. , vol.2 , Issue.1-4 , pp. 311-325
    • Magnus, A.P.1
  • 18
    • 0003984719 scopus 로고
    • Memoirs of the American Mathematical Society, Providence, RI
    • P.G. Nevai, Orthogonal Polynomials, Memoirs of the American Mathematical Society, Providence, RI, 1979.
    • (1979) Orthogonal Polynomials
    • Nevai, P.G.1
  • 19
    • 0004073954 scopus 로고
    • 4th Edition, American Mathematical Society, Providence, RI
    • G. Szego, Orthogonal Polynomials, 4th Edition, American Mathematical Society, Providence, RI, 1975.
    • (1975) Orthogonal Polynomials
    • Szego, G.1
  • 20
    • 24244448277 scopus 로고    scopus 로고
    • Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights, Some new theorems and applications
    • P. Vétesi, Asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights, Some new theorems and applications, Internat. Ser. Numer. Math. 132 (1999) 329-339.
    • (1999) Internat. Ser. Numer. Math. , vol.132 , pp. 329-339
    • Vétesi, P.1
  • 21
    • 0033268189 scopus 로고    scopus 로고
    • Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights
    • P. Vétesi, Uniform asymptotics of derivatives of orthogonal polynomials based on generalized Jacobi weights, Acta Math. Hungar. 85 (1-2) (1999) 97-130.
    • (1999) Acta Math. Hungar. , vol.85 , Issue.1-2 , pp. 97-130
    • Vétesi, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.