메뉴 건너뛰기




Volumn 14, Issue 3, 1998, Pages 439-458

Some indeterminate moment problems and freud-like weights

Author keywords

Asymptotics; Freud weights; Inequalities; Moment problems; Nevanlinna parametrization; Recurrence relations; Zeros

Indexed keywords


EID: 0032370909     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003659900083     Document Type: Article
Times cited : (24)

References (40)
  • 2
    • 21344457626 scopus 로고    scopus 로고
    • On a one-parameter family of q-exponential functions
    • N. M. ATAKISHYIEV (1996): On a one-parameter family of q-exponential functions. J. Phys. A, 29:L223-L227.
    • (1996) J. Phys. A , vol.29
    • Atakishyiev, N.M.1
  • 3
    • 0002733744 scopus 로고
    • Indeterminate moment problems and the theory of entire functions
    • C. BERG (1995): Indeterminate moment problems and the theory of entire functions. J. Comput. Appl. Math., 65:27-55.
    • (1995) J. Comput. Appl. Math. , vol.65 , pp. 27-55
    • Berg, C.1
  • 4
    • 0002914602 scopus 로고
    • Density questions in the classical theory of moments
    • C. BERG, J. P. R. CHRISTENSEN (1981): Density questions in the classical theory of moments. Ann. Inst. Fourier, 31:99-114.
    • (1981) Ann. Inst. Fourier , vol.31 , pp. 99-114
    • Berg, C.1    Christensen, J.P.R.2
  • 6
    • 51249166315 scopus 로고
    • On the order and type of the entire functions associated with an indeterminate Hamburger moment problem
    • C. BERG, H. L. PEDERSEN (1994): On the order and type of the entire functions associated with an indeterminate Hamburger moment problem. Ark. Mat., 32:1-11.
    • (1994) Ark. Mat. , vol.32 , pp. 1-11
    • Berg, C.1    Pedersen, H.L.2
  • 7
    • 0003907038 scopus 로고
    • Nevanlinna extremal measures for some orthogonal polynomials related to birth and death processes
    • C. BERG, G. VALENT (1995): Nevanlinna extremal measures for some orthogonal polynomials related to birth and death processes. J. Comput. Appl. Math., 57:29-43.
    • (1995) J. Comput. Appl. Math. , vol.57 , pp. 29-43
    • Berg, C.1    Valent, G.2
  • 8
    • 0000459042 scopus 로고
    • The nevanlinna parametrization for some indeterminate Stieltjes moment problems associated with birth and death processes
    • C. BERG, G. VALENT (1994): The Nevanlinna parametrization for some indeterminate Stieltjes moment problems associated with birth and death processes. Methods Appl. Anal., 1:169-209.
    • (1994) Methods Appl. Anal. , vol.1 , pp. 169-209
    • Berg, C.1    Valent, G.2
  • 9
    • 85033892393 scopus 로고    scopus 로고
    • Hermitean matrix ensembles and orthogonal polynomials
    • Y. CHEN, M. E. H. ISMAIL (to appear): Hermitean matrix ensembles and orthogonal polynomials. Stud. Appl. Math.
    • Stud. Appl. Math.
    • Chen, Y.1    Ismail, M.E.H.2
  • 10
    • 0001374462 scopus 로고
    • Asymptotics of basic Bessel functions and q-Laguerre polynomials
    • Y. CHEN, M. E. H. ISMAIL, K. A. MUTTALIB (1995): Asymptotics of basic Bessel functions and q-Laguerre polynomials. J. Comput. Appl. Math., 54:263-273.
    • (1995) J. Comput. Appl. Math. , vol.54 , pp. 263-273
    • Chen, Y.1    Ismail, M.E.H.2    Muttalib, K.A.3
  • 12
    • 0000403584 scopus 로고
    • Indeterminate symmetric moment problems
    • T. S. CHIHARA (1982): Indeterminate symmetric moment problems. J. Math. Anal. Appl., 85:331-346.
    • (1982) J. Math. Anal. Appl. , vol.85 , pp. 331-346
    • Chihara, T.S.1
  • 13
    • 35549006412 scopus 로고
    • Statistical theory of energy levels of complex systems, I, II, III
    • F. J. DYSON (1962): Statistical theory of energy levels of complex systems, I, II, III. J. Math. Phys., 3:140-156, 157-165, 166-175.
    • (1962) J. Math. Phys. , vol.3 , pp. 140-156
    • Dyson, F.J.1
  • 16
    • 0000968479 scopus 로고
    • Bounds on the extreme zeros of orthogonal polyomials
    • M. E. H. ISMAIL, X. LI (1992): Bounds on the extreme zeros of orthogonal polyomials. Proc. Amer. Math. Soc., 115:131-140.
    • (1992) Proc. Amer. Math. Soc. , vol.115 , pp. 131-140
    • Ismail, M.E.H.1    Li, X.2
  • 17
    • 0003081035 scopus 로고
    • Q-Hermite polynomials, biorthogonal rational functions and q-beta integrals
    • M. E. H. ISMAIL, D. R. MASSON (1994): q-Hermite polynomials, biorthogonal rational functions and q-beta integrals. Trans. Amer. Math. Soc., 346:61-116.
    • (1994) Trans. Amer. Math. Soc. , vol.346 , pp. 61-116
    • Ismail, M.E.H.1    Masson, D.R.2
  • 18
    • 0001378860 scopus 로고
    • Applications of basic numbers to Bessel's and Legendre 's functions
    • F. H. JACKSON (1904): Applications of basic numbers to Bessel's and Legendre 's functions. Proc. London Math. Soc., (2), 2:192-220.
    • (1904) Proc. London Math. Soc., (2) , vol.2 , pp. 192-220
    • Jackson, F.H.1
  • 19
    • 0000017952 scopus 로고
    • On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials
    • H. T. KOELINK, R. F. SWARTTOUW (1994): On the zeros of the Hahn-Exton q-Bessel function and associated q-Lommel polynomials. J. Math. Anal. Appl., 186:690-710.
    • (1994) J. Math. Anal. Appl. , vol.186 , pp. 690-710
    • Koelink, H.T.1    Swarttouw, R.F.2
  • 20
    • 21344454393 scopus 로고
    • Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function
    • H. T. KOELINK, W. VAN ASSCHE (1995): Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function. Constr. Approx., 11:477-512.
    • (1995) Constr. Approx. , vol.11 , pp. 477-512
    • Koelink, H.T.1    Van Assche, W.2
  • 21
    • 0039482651 scopus 로고
    • Zeta functions, heat kernel expansions, and asymptotics for q-Bessel functions
    • A. A. KVITSINSKI (1995): Zeta functions, heat kernel expansions, and asymptotics for q-Bessel functions. J. Math. Anal. Appl., 196:947-964.
    • (1995) J. Math. Anal. Appl. , vol.196 , pp. 947-964
    • Kvitsinski, A.A.1
  • 23
    • 0038491721 scopus 로고
    • On the asymptotic approximation to integral functions of zero order
    • J. E. LITTLEWOOD (1907): On the asymptotic approximation to integral functions of zero order. Proc. London Math. Soc. (2), 5:361-410. Reprinted in Collected Papers of J. E. Littlewood. Oxford: Oxford University Press, 1982, pp. 1059-1109.
    • (1907) Proc. London Math. Soc. (2) , vol.5 , pp. 361-410
    • Littlewood, J.E.1
  • 24
    • 0038491721 scopus 로고
    • Oxford: Oxford University Press
    • J. E. LITTLEWOOD (1907): On the asymptotic approximation to integral functions of zero order. Proc. London Math. Soc. (2), 5:361-410. Reprinted in Collected Papers of J. E. Littlewood. Oxford: Oxford University Press, 1982, pp. 1059-1109.
    • (1982) Papers of J. E. Littlewood , pp. 1059-1109
  • 25
    • 0000625846 scopus 로고
    • A survey of general orthogonal polynomials for weights on finite and infinite intervals
    • D. S. LUBINSKY (1987): A survey of general orthogonal polynomials for weights on finite and infinite intervals. Acta Appl. Math., 10:237-296.
    • (1987) Acta Appl. Math. , vol.10 , pp. 237-296
    • Lubinsky, D.S.1
  • 26
    • 0001071858 scopus 로고
    • An update on orthogonal polynomials and weighted approximation on the real line
    • D. S. LUBINSKY (1993): An update on orthogonal polynomials and weighted approximation on the real line. Acta Appl. Math., 33:121-164.
    • (1993) Acta Appl. Math. , vol.33 , pp. 121-164
    • Lubinsky, D.S.1
  • 27
    • 0002530588 scopus 로고
    • A proof of Freud's conjecture for exponential weights
    • D. S. LUBINSKY, H. N. MHASKAR, E. B. SAFF (1988): A proof of Freud's conjecture for exponential weights. Constr. Approx., 4:65-83.
    • (1988) Constr. Approx. , vol.4 , pp. 65-83
    • Lubinsky, D.S.1    Mhaskar, H.N.2    Saff, E.B.3
  • 28
    • 0001462684 scopus 로고
    • Asymptotics for the greatest zero of orthogonal polynomials
    • A. MATÉ, P. NEVAL, V. TOTIK (1986): Asymptotics for the greatest zero of orthogonal polynomials. SIAM J. Math. Anal., 17:745-751.
    • (1986) SIAM J. Math. Anal. , vol.17 , pp. 745-751
    • Maté, A.1    Neval, P.2    Totik, V.3
  • 29
    • 84963002147 scopus 로고
    • Asymptotics for the zeros of orthogonal polynomials associated with infinite intervals
    • A. MATÉ, P. NEVAI, V. TOTIK (1986): Asymptotics for the zeros of orthogonal polynomials associated with infinite intervals. J. London Math. Soc. (2), 33:303-310.
    • (1986) J. London Math. Soc. (2) , vol.33 , pp. 303-310
    • A Maté, P.N.1    Totik, V.2
  • 30
    • 84967754997 scopus 로고
    • Extremal problems for polynomials with exponential weight
    • H. N. MHASKAR, E. B. SAFF (1984): Extremal problems for polynomials with exponential weight. Trans. Amer. Math. Soc., 285:203-234.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 203-234
    • Mhaskar, H.N.1    Saff, E.B.2
  • 31
    • 46149132433 scopus 로고
    • Géza Freud, orthogonal polynomials and Christoffel functions. A case study
    • P. NEVAI (1986): Géza Freud, orthogonal polynomials and Christoffel functions. A case study. J. Approx. Theory, 48:3-167.
    • (1986) J. Approx. Theory , vol.48 , pp. 3-167
    • Nevai, P.1
  • 32
    • 0011379835 scopus 로고
    • Asymptotic expansions for q-gamma, q-exponential and q-Bessel functions
    • A. B. OLDE DAALHUIS (1994): Asymptotic expansions for q-gamma, q-exponential and q-Bessel functions. J. Math. Anal. Appl., 186:896-913.
    • (1994) J. Math. Anal. Appl. , vol.186 , pp. 896-913
    • Olde Daalhuis, A.B.1
  • 34
    • 84927422866 scopus 로고
    • On asymptotic properties of polynomials orthogonal on the real axis
    • E. A. RAKHMANOV (1984): On asymptotic properties of polynomials orthogonal on the real axis. Math. USSR-Sb., 47:155-193.
    • (1984) Math. USSR-Sb. , vol.47 , pp. 155-193
    • Rakhmanov, E.A.1
  • 38
    • 0003354741 scopus 로고
    • Asymptotics for orthogonal polynomials
    • Berlin: Springer-Verlag
    • W. VAN ASSCHE (1987): Asymptotics for Orthogonal Polynomials. Lecture Notes in Mathematics, vol. 1265. Berlin: Springer-Verlag.
    • (1987) Lecture Notes in Mathematics , vol.1265
    • Van Assche, W.1
  • 39
    • 0040269675 scopus 로고
    • The ratio of q-like orthogonal polynomials
    • W. VAN ASSCHE (1987): The ratio of q-like orthogonal polynomials. J. Math. Anal. Appl., 128:535-547.
    • (1987) J. Math. Anal. Appl. , vol.128 , pp. 535-547
    • Van Assche, W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.