메뉴 건너뛰기




Volumn 99, Issue 1-2, 1998, Pages 373-385

Orthogonal polynomials with respect to varying weights

Author keywords

Multipoint pad approximation; Orthogonal polynomials; Varying weights

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; INTEGRAL EQUATIONS; INTEGRATION; MATRIX ALGEBRA; PROBABILITY DISTRIBUTIONS; PROBLEM SOLVING; RANDOM PROCESSES;

EID: 0032206805     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00171-X     Document Type: Article
Times cited : (6)

References (29)
  • 2
    • 21844525907 scopus 로고
    • On the statistical mechanics approach in the random matrix theory: Integrated density of states
    • A. Boutet de Monvel, L. Pastur, M. Shcherbina, On the statistical mechanics approach in the random matrix theory: integrated density of states, J. Statist. Phys. 79 (1995) 585-611.
    • (1995) J. Statist. Phys. , vol.79 , pp. 585-611
    • Boutet De Monvel, A.1    Pastur, L.2    Shcherbina, M.3
  • 3
    • 1842689760 scopus 로고    scopus 로고
    • Asymptotics for polynomials orthogonal with respect to varying exponential weights
    • Preprint of the Courant Institute, June 1997
    • P. Deift, T. Kriecherbauer, K.T-R. McLaughlin, S. Venakides, X. Zhou, Asymptotics for polynomials orthogonal with respect to varying exponential weights, Preprint of the Courant Institute, June 1997, Int. Math. Res. Notices 16 (1997) 759-782.
    • (1997) Int. Math. Res. Notices , vol.16 , pp. 759-782
    • Deift, P.1    Kriecherbauer, T.2    McLaughlin, K.T.-R.3    Venakides, S.4    Zhou, X.5
  • 4
    • 0000233635 scopus 로고
    • On Markov's theorem for multipoint Padé approximants
    • A.A. Gonchar, G. Lopez, On Markov's theorem for multipoint Padé approximants, Mat. Sb. 105 (147) (1978). (English transl. Math. USSR Sb. 34 (1978) 449-459.)
    • (1978) Mat. Sb. , vol.105 , Issue.147
    • Gonchar, A.A.1    Lopez, G.2
  • 5
    • 33645338835 scopus 로고
    • English transl.
    • A.A. Gonchar, G. Lopez, On Markov's theorem for multipoint Padé approximants, Mat. Sb. 105 (147) (1978). (English transl. Math. USSR Sb. 34 (1978) 449-459.)
    • (1978) Math. USSR Sb. , vol.34 , pp. 449-459
  • 6
    • 0040198900 scopus 로고    scopus 로고
    • Freud's conjecture and approximation of reciprocals of weights by polynomials
    • A. Knopfmacher, D.S. Lubinsky, P. Nevai, Freud's conjecture and approximation of reciprocals of weights by polynomials, Constr. Approx. 4 (1998) 9-20.
    • (1998) Constr. Approx. , vol.4 , pp. 9-20
    • Knopfmacher, A.1    Lubinsky, D.S.2    Nevai, P.3
  • 7
    • 0030536750 scopus 로고    scopus 로고
    • The role of the endpoint in weighted polynomial approximation with varying weights
    • A.B.J. Kuijlaars, The role of the endpoint in weighted polynomial approximation with varying weights, Constr. Approx. 12 (1996) 287-301.
    • (1996) Constr. Approx. , vol.12 , pp. 287-301
    • Kuijlaars, A.B.J.1
  • 8
    • 0000662099 scopus 로고    scopus 로고
    • A note on weighted polynomial approximation with varying weights
    • A.B.J. Kuijlaars, A note on weighted polynomial approximation with varying weights, J. Approx. Theory 87 (1996) 112-115.
    • (1996) J. Approx. Theory , vol.87 , pp. 112-115
    • Kuijlaars, A.B.J.1
  • 9
    • 0030524947 scopus 로고    scopus 로고
    • Weighted approximation with varying weights: The case of a power-type singularity
    • A.B.J. Kuijlaars, Weighted approximation with varying weights: the case of a power-type singularity, J. Math. Anal. Appl. 204 (1996) 409-418.
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 409-418
    • Kuijlaars, A.B.J.1
  • 10
    • 0009384852 scopus 로고
    • On the asymptotics of the ratio of orthogonal polynomials and the convergence of multipoint Padé approximants
    • G. Lopez, On the asymptotics of the ratio of orthogonal polynomials and the convergence of multipoint Padé approximants, Math. Sb. 128 (1985) 216-229. (Engl. transl. Math. USSR Sb. 56 (1987).)
    • (1985) Math. Sb. , vol.128 , pp. 216-229
    • Lopez, G.1
  • 11
    • 0040555197 scopus 로고
    • Engl. transl.
    • G. Lopez, On the asymptotics of the ratio of orthogonal polynomials and the convergence of multipoint Padé approximants, Math. Sb. 128 (1985) 216-229. (Engl. transl. Math. USSR Sb. 56 (1987).)
    • (1987) Math. USSR Sb. , vol.56
  • 12
    • 0001187532 scopus 로고
    • Asymptotics of polynomials orthogonal with respect to varying measures
    • G. Lopez, Asymptotics of polynomials orthogonal with respect to varying measures, Constr. Approx. 5 (1989) 199-219.
    • (1989) Constr. Approx. , vol.5 , pp. 199-219
    • Lopez, G.1
  • 13
    • 0009156708 scopus 로고
    • Strong asymptotics for extremal errors and polynomials with Erdös type weights
    • Longman Scientific and Technical, New York
    • D.S. Lubinsky, Strong asymptotics for extremal errors and polynomials with Erdös type weights, Pitman Research Notes in Mathematics Series, vol. 202, Longman Scientific and Technical, New York, 1989.
    • (1989) Pitman Research Notes in Mathematics Series , vol.202
    • Lubinsky, D.S.1
  • 14
    • 0002530588 scopus 로고
    • A proof of Freud's conjecture for exponential weights
    • D.S. Lubinsky, H.N. Mhaskar, E.B. Saff, A proof of Freud's conjecture for exponential weights, Constr. Approx. 4 (1988) 65-83.
    • (1988) Constr. Approx. , vol.4 , pp. 65-83
    • Lubinsky, D.S.1    Mhaskar, H.N.2    Saff, E.B.3
  • 15
    • 0003034077 scopus 로고
    • Uniform and mean approximation by certain weighted polynomials, with applications
    • D.S. Lubinsky, E.B. Saff, Uniform and mean approximation by certain weighted polynomials, with applications, Constr. Approx. 4 (1988) 21-64.
    • (1988) Constr. Approx. , vol.4 , pp. 21-64
    • Lubinsky, D.S.1    Saff, E.B.2
  • 16
    • 0003302178 scopus 로고
    • Strong asymptotics for extremal polynomials associated with weights on R
    • Springer, New York
    • D.S. Lubinsky, E.B. Saff, Strong asymptotics for extremal polynomials associated with weights on R, Lecture Notes in Mathematics, vol. 1305, Springer, New York, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1305
    • Lubinsky, D.S.1    Saff, E.B.2
  • 17
    • 21844489247 scopus 로고
    • Weighted polynomial approximation with Freud weights
    • D.S. Lubinsky, V. Totik, Weighted polynomial approximation with Freud weights, Constr. Approx. 10 (1994) 301-315.
    • (1994) Constr. Approx. , vol.10 , pp. 301-315
    • Lubinsky, D.S.1    Totik, V.2
  • 18
    • 0002534477 scopus 로고
    • Where does the sup norm of a weighted polynomial live?
    • H.N. Mhaskar, E.B. Saff, Where does the sup norm of a weighted polynomial live? Constr. Approx. 1 (1985) 71-91.
    • (1985) Constr. Approx. , vol.1 , pp. 71-91
    • Mhaskar, H.N.1    Saff, E.B.2
  • 19
    • 84967754997 scopus 로고
    • Extremal problems for polynomials with exponential weights
    • H.N. Mhaskar, E.B. Saff, Extremal problems for polynomials with exponential weights, Trans. Amer. Math. Soc. 285 (1984) 203-234.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 203-234
    • Mhaskar, H.N.1    Saff, E.B.2
  • 20
    • 46149132433 scopus 로고
    • Orthogonal polynomials and christoffel functions, a case study
    • P. Nevai, Géza Freud, Orthogonal polynomials and Christoffel functions, a case study, J. Approx. Theory 48 (1986) 4-167.
    • (1986) J. Approx. Theory , vol.48 , pp. 4-167
    • Nevai, P.1    Freud, G.2
  • 21
    • 0010114979 scopus 로고    scopus 로고
    • Spectral and probabilistic aspects of matrix models
    • A. Boutet de Monvel, V. Marchenko (Eds.), Kluwer, Dordrecht
    • L. Pastur, Spectral and probabilistic aspects of matrix models, in: A. Boutet de Monvel, V. Marchenko (Eds.), Algebraic and Geometric Methods in Mathematical Physics, Kluwer, Dordrecht, 1996, pp. 207-242.
    • (1996) Algebraic and Geometric Methods in Mathematical Physics , pp. 207-242
    • Pastur, L.1
  • 22
    • 0030684834 scopus 로고    scopus 로고
    • Universality of the local eigenvalue statistics for a class of unitary invariant matrix ensembles
    • L. Pastur, M. Shcherbina, Universality of the local eigenvalue statistics for a class of unitary invariant matrix ensembles, J. Statist. Phys. 86 (1997) 109-147.
    • (1997) J. Statist. Phys. , vol.86 , pp. 109-147
    • Pastur, L.1    Shcherbina, M.2
  • 24
    • 0003329505 scopus 로고
    • General Orthogonal Polynomials
    • Cambridge University Press, New York
    • H. Stahl, V. Totik, General Orthogonal Polynomials, Encyclopedia of Mathematics, vol. 43, Cambridge University Press, New York, 1992.
    • (1992) Encyclopedia of Mathematics , vol.43
    • Stahl, H.1    Totik, V.2
  • 25
    • 0003217929 scopus 로고
    • Orthogonal Polynomials
    • American Mathematical Society, Providence, RI
    • G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloq. Publ., vol. 23, American Mathematical Society, Providence, RI, 1975.
    • (1975) Amer. Math. Soc. Colloq. Publ. , vol.23
    • Szegö, G.1
  • 26
    • 51249163384 scopus 로고
    • Fast decreasing polynomials via potentials
    • V. Totik, Fast decreasing polynomials via potentials, J. Anal. Math. 62 (1994) 131-154.
    • (1994) J. Anal. Math. , vol.62 , pp. 131-154
    • Totik, V.1
  • 27
    • 0003256153 scopus 로고
    • Weighted approximation with varying weights
    • Springer, New York
    • V. Totik, Weighted approximation with varying weights, Lecture Notes in Mathematics, vol. 1569, Springer, New York, 1994.
    • (1994) Lecture Notes in Mathematics , vol.1569
    • Totik, V.1
  • 28
    • 0040555199 scopus 로고
    • Review of the monograph, Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights
    • D.S. Lubinsky (Ed.)
    • V. Totik, Review of the monograph, Strong asymptotics for extremal errors and polynomials associated with Erdös-type weights, D.S. Lubinsky (Ed.), Period. Math. Hungar. 22 (1991) 80-82.
    • (1991) Period. Math. Hungar. , vol.22 , pp. 80-82
    • Totik, V.1
  • 29
    • 0003354741 scopus 로고
    • Asymptotics of orthogonal polynomials
    • Springer, Berlin
    • W. Van Assche, Asymptotics of orthogonal polynomials. Lecture Notes in Mathematics, vol. 1265, Springer, Berlin, 1987.
    • (1987) Lecture Notes in Mathematics , vol.1265
    • Van Assche, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.