메뉴 건너뛰기




Volumn , Issue 7, 2003, Pages 361-385

Zeros of polynomials orthogonal on several intervals

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037509926     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792803208023     Document Type: Article
Times cited : (16)

References (43)
  • 1
    • 0000359984 scopus 로고
    • Orthogonal polynomials on several intervals
    • N. I. Ahiezer, Orthogonal polynomials on several intervals, Soviet Math. Dokl. 1 (1960), 989-992.
    • (1960) Soviet Math. Dokl. , vol.1 , pp. 989-992
    • Ahiezer, N.I.1
  • 2
    • 0001469055 scopus 로고
    • On the theory of orthogonal polynomials over several intervals
    • N. I. Ahiezer and Ju. Ja. Tomčuk, On the theory of orthogonal polynomials over several intervals, Soviet Math. Dokl. 2 (1961), 687-690.
    • (1961) Soviet Math. Dokl. , vol.2 , pp. 687-690
    • Ahiezer, N.I.1    Tomčuk, Ju.Ja.2
  • 3
    • 84956118192 scopus 로고
    • Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices
    • A. I. Aptekarev, Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices, Math. USSR-Sb. 53 (1986), 233-260.
    • (1986) Math. USSR-Sb. , vol.53 , pp. 233-260
    • Aptekarev, A.I.1
  • 4
    • 0033244830 scopus 로고    scopus 로고
    • Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
    • P. Bleher and A. Its, Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model, Ann. of Math. (2) 150 (1999), no. 1, 185-266.
    • (1999) Ann. of Math. (2) , vol.150 , Issue.1 , pp. 185-266
    • Bleher, P.1    Its, A.2
  • 5
    • 0003608444 scopus 로고    scopus 로고
    • Orthogonal polynomials and random matrices: A Riemann-Hilbert approach
    • American Mathematical Society, Rhode Island
    • P. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, American Mathematical Society, Rhode Island, 1998.
    • (1998) Courant Lecture Notes in Mathematics
    • Deift, P.1
  • 6
    • 0000200448 scopus 로고    scopus 로고
    • Integrable systems and combinatorial theory
    • _, Integrable systems and combinatorial theory, Notices Amer. Math. Soc. 47 (2000), no. 6, 631-640.
    • (2000) Notices Amer. Math. Soc. , vol.47 , Issue.6 , pp. 631-640
  • 7
    • 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, and X. Zhou, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Comm. Pure Appl. Math. 52 (1999), no. 11, 1335-1425.
    • (1999) Comm. 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
  • 11
    • 0001412449 scopus 로고
    • Orthogonal polynomials with asymptotically periodic recurrence coefficients
    • J. S. Geronimo and W. Van Assche, Orthogonal polynomials with asymptotically periodic recurrence coefficients, J. Approx. Theory 46 (1986), no. 3, 251-283.
    • (1986) J. Approx. Theory , vol.46 , Issue.3 , pp. 251-283
    • Geronimo, J.S.1    Van Assche, W.2
  • 12
    • 0000196089 scopus 로고
    • On the character of the solution of the moment-problem in the case of the periodic in the limit associated fraction
    • Russian
    • J. Geronimus, On the character of the solution of the moment-problem in the case of the periodic in the limit associated fraction, Izvestia Akad. Nauk SSSR 5 (1941), 203-210 (Russian).
    • (1941) Izvestia Akad. Nauk SSSR , vol.5 , pp. 203-210
    • Geronimus, J.1
  • 13
  • 14
    • 0004092352 scopus 로고
    • Teubner, Leipzig, German, reprinted by Chelsea Publishing Co., New York
    • A. Krazer, Lehrbuch der Thetafunktionen, Teubner, Leipzig, 1903 (German), reprinted by Chelsea Publishing Co., New York, 1970.
    • (1903) Lehrbuch der Thetafunktionen
    • Krazer, A.1
  • 15
    • 0038376879 scopus 로고
    • On special representations of polynomials that are positive on a system of closed intervals, and some applications
    • (Lev. J. Leifman, ed.), Oxford University Press, New York
    • M. G. Kreǐn, B. Ya. Levin, and A. A. Nudel'man, On special representations of polynomials that are positive on a system of closed intervals, and some applications, Functional Analysis, Optimization, and Mathematical Economics (Lev. J. Leifman, ed.), Oxford University Press, New York, 1990, pp. 56-114.
    • (1990) Functional Analysis, Optimization, and Mathematical Economics , pp. 56-114
    • Kreǐn, M.G.1    Levin, B.Ya.2    Nudel'Man, A.A.3
  • 20
    • 0000154513 scopus 로고
    • Recurrence coefficients for orthogonal polynomials on connected and nonconnected sets
    • Padé Approximation and Its Applications, Proc. Conf., Univ. Antwerp, Antwerp, Springer, Berlin, 1979
    • A. Magnus, Recurrence coefficients for orthogonal polynomials on connected and nonconnected sets, Padé Approximation and Its Applications (Proc. Conf., Univ. Antwerp, Antwerp, 1979), Lecture Notes in Math., vol. 765, Springer, Berlin, 1979, pp. 150-171.
    • (1979) Lecture Notes in Math. , vol.765 , pp. 150-171
    • Magnus, A.1
  • 21
    • 0038376880 scopus 로고
    • Sur les racines de certaines équations
    • French
    • A. Markoff, Sur les racines de certaines équations, Math. Ann. 27 (1886), 143-150 (French).
    • (1886) Math. Ann. , vol.27 , pp. 143-150
    • Markoff, A.1
  • 22
    • 0038715251 scopus 로고
    • Singuläre integralgleichungen. Randwertprobleme der funktionentheorie und einige anwendungen auf die mathematische physik
    • Akademie-Verlag, Berlin (German)
    • N. I. Muschelischwili, Singuläre Integralgleichungen. Randwertprobleme der Funktionentheorie und einige Anwendungen auf die mathematische Physik, Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien, vol. 20, Akademie-Verlag, Berlin, 1965 (German).
    • (1965) Mathematische Lehrbücher und Monographien, II. Abteilung, Mathematische Monographien , vol.20
    • Muschelischwili, N.I.1
  • 23
    • 0002690722 scopus 로고
    • Orthogonal polynomials and Padé approximants associated with a system of arcs
    • J. Nuttall and S. R. Singh, Orthogonal polynomials and Padé approximants associated with a system of arcs, J. Approximation Theory 21 (1977), no. 1, 1-42.
    • (1977) J. Approximation Theory , vol.21 , Issue.1 , pp. 1-42
    • Nuttall, J.1    Singh, S.R.2
  • 25
    • 0010114979 scopus 로고    scopus 로고
    • Spectral and probabilistic aspects of matrix models
    • Algebraic and Geometric Methods in Mathematical Physics (Kaciveli, 1993) (A. Boutet de Monvel and V. Marchenko, eds.) Kluwer Academic Publishers, Dordrecht
    • L. A. Pastur, Spectral and probabilistic aspects of matrix models, Algebraic and Geometric Methods in Mathematical Physics (Kaciveli, 1993) (A. Boutet de Monvel and V. Marchenko, eds.), Math. Phys. Stud., vol. 19, Kluwer Academic Publishers, Dordrecht, 1996, pp. 207-242.
    • (1996) Math. Phys. Stud. , vol.19 , pp. 207-242
    • Pastur, L.A.1
  • 26
    • 0030684834 scopus 로고    scopus 로고
    • Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles
    • L. A. Pastur and M. Shcherbina, Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles, J. Statist. Phys. 86 (1997), no. 1-2, 109-147.
    • (1997) J. Statist. Phys. , vol.86 , Issue.1-2 , pp. 109-147
    • Pastur, L.A.1    Shcherbina, M.2
  • 27
    • 0000561029 scopus 로고
    • On Bernstein-Szego orthogonal polynomials on several intervals
    • F. Peherstorfer, On Bernstein-Szego orthogonal polynomials on several intervals, SIAM J. Math. Anal. 21 (1990), no. 2, 461-482.
    • (1990) SIAM J. Math. Anal. , vol.21 , Issue.2 , pp. 461-482
    • Peherstorfer, F.1
  • 28
    • 0000548215 scopus 로고
    • On Bernstein-Szego orthogonal polynomials on several intervals. II. Orthogonal polynomials with periodic recurrence coefficients
    • _, On Bernstein-Szego orthogonal polynomials on several intervals. II. Orthogonal polynomials with periodic recurrence coefficients, J. Approx. Theory 64 (1991), no. 2, 123-161.
    • (1991) J. Approx. Theory , vol.64 , Issue.2 , pp. 123-161
  • 29
    • 0001091986 scopus 로고
    • Orthogonal and extremal polynomials on several intervals
    • _, Orthogonal and extremal polynomials on several intervals, J. Comput. Appl. Math. 48 (1993), no. 1-2, 187-205.
    • (1993) J. Comput. Appl. Math. , vol.48 , Issue.1-2 , pp. 187-205
  • 30
    • 0001198516 scopus 로고
    • Elliptic orthogonal and extremal polynomials
    • _, Elliptic orthogonal and extremal polynomials, Proc. London Math. Soc. (3) 70 (1995), no. 3, 605-624.
    • (1995) Proc. London Math. Soc. (3) , vol.70 , Issue.3 , pp. 605-624
  • 33
    • 0011611015 scopus 로고
    • On polynomials orthogonal on several intervals
    • F. Peherstorfer and R. Steinbauer, On polynomials orthogonal on several intervals, Ann. Numer. Math. 2 (1995), no. 1-4, 353-370.
    • (1995) Ann. Numer. Math. , vol.2 , Issue.1-4 , pp. 353-370
    • Peherstorfer, F.1    Steinbauer, R.2
  • 34
    • 33645894379 scopus 로고    scopus 로고
    • Asymptotic behaviour of polynomials orthonormal on a homogeneous set
    • F. Peherstorfer and P. Yuditskii, Asymptotic behaviour of polynomials orthonormal on a homogeneous set, to appear in J. Anal. Math.
    • J. Anal. Math.
    • Peherstorfer, F.1    Yuditskii, P.2
  • 35
    • 0038376905 scopus 로고
    • Orthogonal polynomials for nonclassical weight functions
    • T. E. Price Jr., Orthogonal polynomials for nonclassical weight functions, SIAM J. Numer. Anal. 16 (1979), no. 6, 999-1006.
    • (1979) SIAM J. Numer. Anal. , vol.16 , Issue.6 , pp. 999-1006
    • Price T.E., Jr.1
  • 36
    • 0003221535 scopus 로고
    • Potential theory in the complex plane
    • Cambridge University Press, Cambridge
    • T. Ransford, Potential Theory in the Complex Plane, London Mathematical Society Student Texts, vol. 28, Cambridge University Press, Cambridge, 1995.
    • (1995) London Mathematical Society Student Texts , vol.28
    • Ransford, T.1
  • 38
  • 39
    • 0003822511 scopus 로고
    • Introduction to Riemann surfaces
    • Addison-Wesley, Massachusetts
    • G. Springer, Introduction to Riemann Surfaces, Addison-Wesley Math. Series, Addison-Wesley, Massachusetts, 1957.
    • (1957) Addison-Wesley Math. Series
    • Springer, G.1
  • 40
    • 0034341570 scopus 로고    scopus 로고
    • Uniform convergence of Padé diagonal approximants for hyperelliptic functions
    • S. P. Suetin, Uniform convergence of Padé diagonal approximants for hyperelliptic functions, Sb. Math. 191 (2000), no. 9, 1339-1373.
    • (2000) Sb. Math. , vol.191 , Issue.9 , pp. 1339-1373
    • Suetin, S.P.1
  • 41
    • 0004073954 scopus 로고
    • American Mathematical Society, Colloquium Publications, American Mathematical Society, Rhode Island
    • G. Szegö, Orthogonal Polynomials, American Mathematical Society, Colloquium Publications, vol. 23, American Mathematical Society, Rhode Island, 1975.
    • (1975) Orthogonal Polynomials , vol.23
    • Szegö, G.1
  • 42
    • 4243991611 scopus 로고
    • Orthogonal polynomials on a system of intervals of the real axis
    • Ju. Ja. Tomčuk, Orthogonal polynomials on a system of intervals of the real axis, Zap. Mekh.-Math. Fak. i Kharkov. Mat. Obshch. 29 (1964), no. 4, 93-128.
    • (1964) Zap. Mekh.-Math. Fak. i Kharkov. Mat. Obshch. , vol.29 , Issue.4 , pp. 93-128
    • Tomčuk, Ju.Ja.1
  • 43
    • 0002059690 scopus 로고
    • Extremal polynomials associated with a system of curves in the complex plane
    • H. Widom, Extremal polynomials associated with a system of curves in the complex plane, Advances in Math. 3 (1969), 127-232.
    • (1969) Advances in Math. , vol.3 , pp. 127-232
    • Widom, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.