메뉴 건너뛰기




Volumn 127, Issue 1-2, 2001, Pages 17-65

Complex Jacobi matrices

Author keywords

30B70; 39A70; 41A21; 47B39; Complex Jacobi matrix; Convergence of J fractions; Difference operator; Formal orthogonal polynomials; Pad approximation; Resolvent convergence

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; COMPUTATIONAL METHODS; ITERATIVE METHODS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA;

EID: 0035148389     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00492-1     Document Type: Article
Times cited : (68)

References (60)
  • 3
    • 0040687512 scopus 로고    scopus 로고
    • The spectrum of a periodic complex Jacobi matrix revisited
    • to appear
    • A. Almendral Vázquez, The spectrum of a periodic complex Jacobi matrix revisited, J. Approx. Theory, to appear.
    • J. Approx. Theory
    • Almendral Vázquez, A.1
  • 4
    • 0000126692 scopus 로고
    • On exceptional sets of asymptotic relations for general orthogonal polynomials
    • Ambroladze A. On exceptional sets of asymptotic relations for general orthogonal polynomials. J. Approx. Theory. 82:1995;257-273.
    • (1995) J. Approx. Theory , vol.82 , pp. 257-273
    • Ambroladze, A.1
  • 5
    • 0032206942 scopus 로고    scopus 로고
    • Multiple orthogonal polynomials
    • Aptekarev A.I. Multiple orthogonal polynomials. J. Comput. Appl. Math. 99:1998;423-447.
    • (1998) J. Comput. Appl. Math. , vol.99 , pp. 423-447
    • Aptekarev, A.I.1
  • 7
    • 84966238927 scopus 로고
    • Criterion for the resolvent set of nonsymmetric tridiagonal operators
    • Aptekarev A.I., Kaliaguine V.A., Van Assche W. Criterion for the resolvent set of nonsymmetric tridiagonal operators. Proc. Amer. Math. Soc. 123:1995;2423-2430.
    • (1995) Proc. Amer. Math. Soc. , vol.123 , pp. 2423-2430
    • Aptekarev, A.I.1    Kaliaguine, V.A.2    Van Assche, W.3
  • 8
    • 0034337982 scopus 로고    scopus 로고
    • Genetic sum representation for the moments of a system of Stieltjes functions and its application
    • to appear
    • A.I. Aptekarev, V.A. Kaliaguine, J. Van Iseghem, Genetic sum representation for the moments of a system of Stieltjes functions and its application, Constr. Approx., to appear.
    • Constr. Approx.
    • Aptekarev, A.I.1    Kaliaguine, V.A.2    Van Iseghem, J.3
  • 9
    • 0037482488 scopus 로고
    • The Padé tables and continued fraction representations generated by totally positive sequences
    • Ohio University Press, Athens, OH
    • R.J. Arms, A. Edrei, The Padé tables and continued fraction representations generated by totally positive sequences in: Mathematical Essays, Ohio University Press, Athens, OH, 1970, pp. 1-21.
    • (1970) In: Mathematical Essays , pp. 1-21
    • Arms, R.J.1    Edrei, A.2
  • 12
    • 0040093978 scopus 로고    scopus 로고
    • personal communication, June
    • L. Baratchart, personal communication, June 1999.
    • (1999)
    • Baratchart, L.1
  • 13
    • 0000864053 scopus 로고    scopus 로고
    • On the domain of convergence and poles of complex J -fractions
    • Barrios D., López G., Martínez A., Torrano E. On the domain of convergence and poles of complex. J -fractions J. Approx. Theory. 93:1998;177-200.
    • (1998) J. Approx. Theory , vol.93 , pp. 177-200
    • Barrios, D.1    López, G.2    Martínez, A.3    Torrano, E.4
  • 14
    • 0033472748 scopus 로고    scopus 로고
    • Finite-dimensional approximations of the resolvent of an infinite banded matrix and continued fractions
    • Barrios D., López G., Martínez A., Torrano E. Finite-dimensional approximations of the resolvent of an infinite banded matrix and continued fractions. Sbornik: Mathematics. 190:1999;501-519.
    • (1999) Sbornik: Mathematics , vol.190 , pp. 501-519
    • Barrios, D.1    López, G.2    Martínez, A.3    Torrano, E.4
  • 15
    • 84956224642 scopus 로고
    • Location of zeros and asymptotics of polynomials defined by three-term recurrence relation with complex coefficients
    • Barrios D., López G., Torrano E. Location of zeros and asymptotics of polynomials defined by three-term recurrence relation with complex coefficients. Russian Acad. Sci. Sb. Math. 80:1995;309-333.
    • (1995) Russian Acad. Sci. Sb. Math. , vol.80 , pp. 309-333
    • Barrios, D.1    López, G.2    Torrano, E.3
  • 16
    • 84957134163 scopus 로고
    • Polynomials generated by asymptotically periodic complex recurrence coefficients
    • Barrios D., López G., Torrano E. Polynomials generated by asymptotically periodic complex recurrence coefficients. Sbornik: Mathematics. 186:1995;629-660.
    • (1995) Sbornik: Mathematics , vol.186 , pp. 629-660
    • Barrios, D.1    López, G.2    Torrano, E.3
  • 17
    • 84953818707 scopus 로고
    • A norm inequality for a finite-section Wiener-Hopf equation
    • Baxter G. A norm inequality for a finite-section Wiener-Hopf equation. Illinois Math. 7:1963;97-103.
    • (1963) Illinois Math. , vol.7 , pp. 97-103
    • Baxter, G.1
  • 18
    • 0039047553 scopus 로고    scopus 로고
    • On the convergence of bounded J -fractions on the resolvent set of the corresponding second order difference operator
    • Beckermann B. On the convergence of bounded. J -fractions on the resolvent set of the corresponding second order difference operator J. Approx. Theory. 99:1999;369-408.
    • (1999) J. Approx. Theory , vol.99 , pp. 369-408
    • Beckermann, B.1
  • 19
    • 85088006658 scopus 로고    scopus 로고
    • On the classification of the spectrum of second order difference operators
    • Publication ANO 379, Université de Lille, to appear
    • B. Beckermann, On the classification of the spectrum of second order difference operators, Publication ANO 379, Université de Lille, 1997 Math. Nachr., to appear.
    • 1997 Math. Nachr.
    • Beckermann, B.1
  • 20
    • 0031530039 scopus 로고    scopus 로고
    • The diagonal of the Padé table and the approximation of the Weyl function of second order difference operators
    • Beckermann B., Kaliaguine V.A. The diagonal of the Padé table and the approximation of the Weyl function of second order difference operators. Constr. Approx. 13:1997;481-510.
    • (1997) Constr. Approx. , vol.13 , pp. 481-510
    • Beckermann, B.1    Kaliaguine, V.A.2
  • 21
    • 0000471705 scopus 로고
    • Integration of nonlinear difference equation by the inverse spectral problem method
    • Berezanskii Yu.M. Integration of nonlinear difference equation by the inverse spectral problem method. Soviet Mathem. Dokl. 31(2):1985;264-267.
    • (1985) Soviet Mathem. Dokl. , vol.31 , Issue.2 , pp. 264-267
    • Berezanskii, Yu.m.1
  • 22
    • 0040093974 scopus 로고    scopus 로고
    • Determinacy of bounded complex perturbations of Jacobi matrices
    • to appear
    • M. Castro Smirnova, Determinacy of bounded complex perturbations of Jacobi matrices, J. Approx. Theory, to appear.
    • J. Approx. Theory
    • Castro Smirnova, M.1
  • 23
    • 84966252352 scopus 로고
    • Decay rates for inverses of band matrices
    • Demko S., Moss W.F., Smith P.W. Decay rates for inverses of band matrices. Math. Comp. 43:1984;491-499.
    • (1984) Math. Comp. , vol.43 , pp. 491-499
    • Demko, S.1    Moss, W.F.2    Smith, P.W.3
  • 24
    • 0001412449 scopus 로고
    • Orthogonal polynomials with asymptotically periodic recurrence coefficients
    • Geronimo J., Van Assche W. Orthogonal polynomials with asymptotically periodic recurrence coefficients. J. Approx. Theory. 46:1986;251-283.
    • (1986) J. Approx. Theory , vol.46 , pp. 251-283
    • Geronimo, J.1    Van Assche, W.2
  • 25
    • 0006841979 scopus 로고
    • On the asymptotic distribution of eigenvalues of banded matrices
    • Geronimo J.S., Harrell II E.M., Van Assche W. On the asymptotic distribution of eigenvalues of banded matrices. Constr. Approx. 4:1988;403-417.
    • (1988) Constr. Approx. , vol.4 , pp. 403-417
    • Geronimo, J.S.1    Harrell E.M. II2    Van Assche, W.3
  • 27
    • 0008447075 scopus 로고
    • On the numerical radius and its applications
    • Goldberg M., Tadmor E. On the numerical radius and its applications. Linear Algebra Appl. 42:1982;263-284.
    • (1982) Linear Algebra Appl. , vol.42 , pp. 263-284
    • Goldberg, M.1    Tadmor, E.2
  • 28
    • 84956074063 scopus 로고
    • On uniform convergence of diagonal Padé approximants
    • Gonchar A.A. On uniform convergence of diagonal Padé approximants. Math. USSR Sb. 46:1983;539-559.
    • (1983) Math. USSR Sb. , vol.46 , pp. 539-559
    • Gonchar, A.A.1
  • 29
    • 0040093976 scopus 로고
    • On rational approximation of the resolvent function of second order difference operator
    • Kaliaguine V.A. On rational approximation of the resolvent function of second order difference operator. Russian Math. Surveys. 49(3):1994;187-189.
    • (1994) Russian Math. Surveys , vol.49 , Issue.3 , pp. 187-189
    • Kaliaguine, V.A.1
  • 31
    • 0001114597 scopus 로고    scopus 로고
    • The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients
    • Kuijlaars A.B.J., Van Assche W. The asymptotic zero distribution of orthogonal polynomials with varying recurrence coefficients. J. Approx. Theory. 99:1999;167-197.
    • (1999) J. Approx. Theory , vol.99 , pp. 167-197
    • Kuijlaars, A.B.J.1    Van Assche, W.2
  • 33
    • 0023378727 scopus 로고
    • Toeplitz matrix techniques and convergence of complex weight Padé approximants
    • Magnus A.P. Toeplitz matrix techniques and convergence of complex weight Padé approximants. J. Comput. Appl. Math. 19:1987;23-38.
    • (1987) J. Comput. Appl. Math. , vol.19 , pp. 23-38
    • Magnus, A.P.1
  • 34
    • 0001530319 scopus 로고
    • The supports of measures associated with orthogonal polynomials and the spectra of the related self adjoint operators
    • Máté A., Nevai P., Van Assche W. The supports of measures associated with orthogonal polynomials and the spectra of the related self adjoint operators. Rocky Mountain J. Math. 21:1991;501-527.
    • (1991) Rocky Mountain J. Math. , vol.21 , pp. 501-527
    • Máté, A.1    Nevai, P.2    Van Assche, W.3
  • 35
    • 0000956929 scopus 로고
    • Orthogonal Polynomials
    • Providence, RI: AMS
    • Nevai P. Orthogonal Polynomials. Memoirs Amer. Math. Soc. Vol. 213:1979;AMS, Providence, RI.
    • (1979) Memoirs Amer. Math. Soc. , vol.213
    • Nevai, P.1
  • 36
    • 84974001035 scopus 로고
    • Compact perturbations of orthogonal polynomials
    • Nevai P., Van Assche W. Compact perturbations of orthogonal polynomials. Parcific J. Math. 153:1992;163-184.
    • (1992) Parcific J. Math. , vol.153 , pp. 163-184
    • Nevai, P.1    Van Assche, W.2
  • 37
    • 0000023186 scopus 로고
    • Discrete Sturm-Liouville operators and some problems of function theory
    • Nikishin E.M. Discrete Sturm-Liouville operators and some problems of function theory. J. Soviet Math. 35:1986;2679-2744.
    • (1986) J. Soviet Math. , vol.35 , pp. 2679-2744
    • Nikishin, E.M.1
  • 39
    • 0000978332 scopus 로고
    • Padé polynomial asymptotics from a singular integral equation
    • Nuttall J. Padé polynomial asymptotics from a singular integral equation. Constr. Approx. 6:1990;157-166.
    • (1990) Constr. Approx. , vol.6 , pp. 157-166
    • Nuttall, J.1
  • 40
    • 0000503195 scopus 로고
    • Gaussian integration for complex weight functions
    • Nuttall J., Wherry C.J. Gaussian integration for complex weight functions. J. Inst. Math. Appl. 21:1978;165-170.
    • (1978) J. Inst. Math. Appl. , vol.21 , pp. 165-170
    • Nuttall, J.1    Wherry, C.J.2
  • 42
    • 0002199277 scopus 로고
    • Moment problems and operators in Hilbert spaces
    • D. Sarason, Moment problems and operators in Hilbert spaces. Proc. Symp. Appl. Math. 37, 1987, pp. 54-70.
    • (1987) Proc. Symp. Appl. Math. , vol.37 , pp. 54-70
    • Sarason, D.1
  • 43
    • 0003723155 scopus 로고
    • New York: Universitext, Springer
    • Schiff J.L. Normal Families. 1993;Universitext, Springer, New York.
    • (1993) Normal Families
    • Schiff, J.L.1
  • 44
  • 45
    • 0002672593 scopus 로고    scopus 로고
    • The classical moment problem as a self-adjoint finite difference operator
    • Simon B. The classical moment problem as a self-adjoint finite difference operator. Adv. Math. 137:1998;82-203.
    • (1998) Adv. Math. , vol.137 , pp. 82-203
    • Simon, B.1
  • 46
    • 0039622875 scopus 로고
    • Divergence of diagonal Padé approximants and the asymptotic behavior of orthogonal polynomials associated with nonpositive measures
    • Stahl H. Divergence of diagonal Padé approximants and the asymptotic behavior of orthogonal polynomials associated with nonpositive measures. Constr. Approx. 1:1985;249-270.
    • (1985) Constr. Approx. , vol.1 , pp. 249-270
    • Stahl, H.1
  • 48
    • 0040645447 scopus 로고    scopus 로고
    • Conjectures around the Baker-Gammel-Wills conjecture
    • Stahl H. Conjectures around the Baker-Gammel-Wills conjecture. Constr. Approx. 13:1997;287-292.
    • (1997) Constr. Approx. , vol.13 , pp. 287-292
    • Stahl, H.1
  • 49
    • 0000152468 scopus 로고    scopus 로고
    • The convergence of Padé approximants to functions with branch points
    • Stahl H. The convergence of Padé approximants to functions with branch points. J. Approx. Theory. 91:1997;139-204.
    • (1997) J. Approx. Theory , vol.91 , pp. 139-204
    • Stahl, H.1
  • 50
    • 0032207667 scopus 로고    scopus 로고
    • Spurious poles in Padé approximation
    • Stahl H. Spurious poles in Padé approximation. J. Comput. Appl. Math. 99:1998;511-527.
    • (1998) J. Comput. Appl. Math. , vol.99 , pp. 511-527
    • Stahl, H.1
  • 53
    • 0039878891 scopus 로고
    • A lower bound for orthogonal polynomials with an application to polynomial hypergroups
    • Szwarc R. A lower bound for orthogonal polynomials with an application to polynomial hypergroups. J. Approx. Theory. 81:1995;145-150.
    • (1995) J. Approx. Theory , vol.81 , pp. 145-150
    • Szwarc, R.1
  • 54
    • 21844500007 scopus 로고
    • A counterexample to subexponential growth of orthogonal polynomials
    • Szwarc R. A counterexample to subexponential growth of orthogonal polynomials. Constr. Approx. 11:1995;381-389.
    • (1995) Constr. Approx. , vol.11 , pp. 381-389
    • Szwarc, R.1
  • 56
    • 0001537694 scopus 로고
    • Orthogonal polynomials, associated polynomials and functions of the second kind
    • Van Assche W. Orthogonal polynomials, associated polynomials and functions of the second kind. J. Comput. Appl. Math. 37:1991;237-249.
    • (1991) J. Comput. Appl. Math. , vol.37 , pp. 237-249
    • Van Assche, W.1
  • 58
    • 0004577430 scopus 로고
    • Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices
    • van Doorn E.A. Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices. J. Approx. Theory. 51:1987;254-266.
    • (1987) J. Approx. Theory , vol.51 , pp. 254-266
    • Van Doorn, E.A.1
  • 60
    • 0032379803 scopus 로고    scopus 로고
    • Normal families: New perspectives
    • Zalcman L. Normal families: new perspectives. Bull. Amer. Math. Soc. 35:1998;215-230.
    • (1998) Bull. Amer. Math. Soc. , vol.35 , pp. 215-230
    • Zalcman, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.