Browse issues
Compact Jacobi matrices : from Stieltjes to Krein and M(a,b)
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume S5 (1996), pp. 195-215. 
@article{AFST_1996_6_S5__195_0,
     author = {Walter Van Assche},
     title = {Compact {Jacobi} matrices : from {Stieltjes} to {Krein} and $M(a, b)$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {195--215},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, S5},
     year = {1996},
     zbl = {0879.42013},
     mrnumber = {1462710},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_1996_6_S5__195_0/}
}
TY  - JOUR
AU  - Walter Van Assche
TI  - Compact Jacobi matrices : from Stieltjes to Krein and $M(a, b)$
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 1996
SP  - 195
EP  - 215
VL  - S5
PB  - Université Paul Sabatier, Institut de Mathématiques
PP  - Toulouse
UR  - https://afst.centre-mersenne.org/item/AFST_1996_6_S5__195_0/
LA  - en
ID  - AFST_1996_6_S5__195_0
ER  - 
%0 Journal Article
%A Walter Van Assche
%T Compact Jacobi matrices : from Stieltjes to Krein and $M(a, b)$
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 1996
%P 195-215
%V S5
%I Université Paul Sabatier, Institut de Mathématiques
%C Toulouse
%U https://afst.centre-mersenne.org/item/AFST_1996_6_S5__195_0/
%G en
%F AFST_1996_6_S5__195_0
Walter Van Assche. Compact Jacobi matrices : from Stieltjes to Krein and $M(a, b)$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume S5 (1996), pp. 195-215. https://afst.centre-mersenne.org/item/AFST_1996_6_S5__195_0/

[1] Akhiezer (N.I. ) and Glazman (I.M.).- Theory of Linear Operators in Hilbert Space, vol. I, Pitman, Boston, 1981. | Zbl

[2] Al-Salam (W. A.) and Ismail (M.E.H.).- Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction, Pacific J. Math. 104 (1983), pp. 269-283. | MR | Zbl

[3] Askey (R.) and Ismail ( M.). - Recurrence relations, continued fractions and orthogonal polynomials, Memoirs Amer. Math. Soc. 300, Providence, RI, 1984 . | Zbl

[4] Blumenthal ( O. ).- Ueber die Entwicklung einer willkürlichen Funktion nach den Nennern des Ket tenbruches für ∫0-∞ ϕ(ξ)/(z - ξ) dξ, Inaugural-Dissertation. Göttingen, 1898. | JFM

[5] Chihara (T.S.).- An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978. | MR | Zbl

[6] Chihara (T.S. ) and Ismail (M.E.H.).- Orthogonal polynomials suggested by a queueing model, Adv. Appl. Math. 3 (1982), pp. 441-462. | MR | Zbl

[7] Dickinson ( D.).- On Lommel and Bessel polynomials , Proc. Amer. Math. Soc. 5 (1954), pp. 946-956. | MR | Zbl

[8] Dickinson ( D.J.), Pollak (H.O.) and Wannier (G.H.).- On a class of polynomials orthogonal over a denumerable set, Pacific J. Math. 6 (1956), pp. 239-247. | MR | Zbl

[9] Dombrowski ( J. ).- Orthogonal polynomials and functional analysis, in "Orthogonal Polynomials: Theory and Practice" (P. Nevai, ed.), NATO-ASI series C 294, Kluwer, Dordrecht, 1990, pp. 147-161. | MR | Zbl

[10] Dunford (N. ) and Schwartz ( J.T.).- Linear Operators, Part II: Spectral theory. Self Adjoint Operators in Hilbert Space, Interscience Publishers (John Wiley & Sons), New York, 1963. | MR | Zbl

[11] Durán (A.J. ) and Van Assche (W.).- Orthogonal matrix polynomials and higher-order recurrence relations, Linear Algebra Appl. 219 (1995 ), pp. 261-280. | MR | Zbl

[12] Goh (W.M.Y. ) and Wimp (J.).- On the asymptotics of the Tricomi-Carlitz polynomials and their zero distribution (I, SIAM J. Math. Anal. 25 ( 1994). pp. 420-428. | MR | Zbl

[13] Goldberg ( J.L.).- Polynomials orthogonal over a denumerable set, Pacific J. Math. 15, n° 4 (1965), pp. 1171-1186. | MR | Zbl

[14] Ismail (M.E.H. ).- The zeros of basic Bessel functions, the functions Jν+ax(x), and associated orthogonal polynomials , J. Math. Anal. Appl. 86 (1982), pp. 1-19. | Zbl

[15] Kato (T.). - Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966. | MR | Zbl

[16] Koelink ( H.T.) and Van Assche (W.).- Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function , Constr. Approx. 11 (1995), pp. 477-512. | MR | Zbl

[17] Koekoek (R. ) and Swarttouw ( R.F.).- The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Reports of the Faculty of Technical Mathematics and Informatics 94-05, Delft University of Technology, 1994, 120 pp.

[18] Kreĭn ( M.). - Concerning a special class of entire and meromorphic functions, in "O nekotorykh voprosakh teorii momentov'' (N. Akhiezer, M. Kreĭn), Nauchno-Tekhnicheskoe Izdatelstvo Ukrainy, Kharkov, 1938 ; translated in "Some questions in the theory of moments" ( N. I. Ahiezer, M. Kreĭn ), Translations of Mathematical Monographs. Vol. 2, Amer. Math. Soc., Providence, RI 1962, pp. 241-265.

[19] Máté ( A.) and Nevai ( P.). - A generalization of Poincaré's theorem for recurrence relations, J. Approx. Theory 63 (1990), pp. 92-97. | MR | Zbl

[20] Máté ( A.) , Nevai ( P.) and 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), pp. 501-527. | MR | Zbl

[21] Nevai (P. ).- Orthogonal Polynomials, Memoirs Amer. Math. Soc. 213, Providence, RI, 1979. | MR | Zbl

[22] Poincaré (H. ). - Sur les équations linéaires aux différentielles et aux différences finies, Amer. J. Math. 7 (1885), pp. 203-258. | JFM | MR

[23] Schwartz (H.M. ).- A class of continued fractions, Duke Math. J. 6 (1940), pp. 48-65. | JFM | MR | Zbl

[24] Sleshinskii ( I.V.).- Convergence of continued fractions , Zap. Mat. Otod. Novoros. Obshchest. 8 (1888), pp. 97-127.

[25] Stieltjes ( T.J.).- Recherches sur les fractions continues , Ann. Fac. Sci. Toulouse 8 (1894), pp. J1-122; 9 (1895 ), pp. A1-47; Œuvres Complètes-Collected Papers, Vol. II (G. van Dijk , ed.), Springer-Verlag, Berlin , 1993, pp. 406-570 (English translation on pp. 609-745). | JFM | Numdam

[26] Stone (M.H. ).- Linear Transformations in Hilbert Space and their Applications to Analysis, Amer. Math. Soc. Colloq. Publ. 15, Providence, RI, 1932. | JFM | MR

[27] Thron (W.J. ). - Some results on separate convergence of continued fractions , in "Computational Methods and Function Theory" (St. Ruschewey et al., eds.), Lecture Notes in Mathematics 1435, Springer-Verlag, Berlin, 1990, pp. 191-200. | MR | Zbl

[28] Van Assche ( W. ). - Asymptotics of orthogonal polynomials and three-term recurrences, in "Orthogonal Polynomials: Theory and Practice" (P. Nevai, ed.), NATO-ASI series C 294, Kluwer, Dordrecht, 1990 , pp. 435-462. | MR | Zbl

[29] Van Doorn ( E.A.).- The transient state probabilities for a queueing model where potential customers are discouraged by queue length , J. Appl. Prob. 18 ( 1981), pp. 499-506. | MR | Zbl

[30] Van Vleck ( E.B.).- On the convergence of the continued fraction of Gauss and other continued fractions, Annals of Math. (2) 3 (1901), pp. 1-18. | JFM | MR

[31] Van Vleck ( E.B.).- On the convergence of algebraic continued fractions whose coefficients have limiting values, Trans. Amer. Math. Soc. 5 (1904 ), pp. 253-262. | JFM | MR

[32] Wall (H.S. ). - On continued fractions which represent meromorphic functions, Bull. Amer. Math. Soc. 39 (1933), pp. 946-952. | JFM | Zbl

[33] Wall (H.S. ). - On the continued fractions of the form K∞1(bνz/1, Bull. Amer. Math. Soc. 41 (1935), pp. 727-736. | Zbl