@article{AFST_1996_6_S5__195_0, author = {Van Assche, Walter}, 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}, mrnumber = {1462710}, zbl = {0879.42013}, language = {en}, url = {http://www.numdam.org/item/AFST_1996_6_S5__195_0/} }
TY - JOUR AU - Van Assche, Walter 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 - http://www.numdam.org/item/AFST_1996_6_S5__195_0/ LA - en ID - AFST_1996_6_S5__195_0 ER -
%0 Journal Article %A Van Assche, Walter %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 http://www.numdam.org/item/AFST_1996_6_S5__195_0/ %G en %F AFST_1996_6_S5__195_0
Van Assche, Walter. Compact Jacobi matrices : from Stieltjes to Krein and $M(a, b)$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome S5 (1996), pp. 195-215. http://www.numdam.org/item/AFST_1996_6_S5__195_0/
[1] Theory of Linear Operators in Hilbert Space, vol. I, Pitman, Boston, 1981. | Zbl
and -[2] Orthogonal polynomials associated with the Rogers-Ramanujan continued fraction, Pacific J. Math. 104 (1983), pp. 269-283. | MR | Zbl
and -[3] Recurrence relations, continued fractions and orthogonal polynomials, Memoirs Amer. Math. Soc. 300, Providence, RI, 1984 . | Zbl
and -[4] 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] An Introduction to Orthogonal Polynomials, Gordon and Breach, New York, 1978. | MR | Zbl
-[6] Orthogonal polynomials suggested by a queueing model, Adv. Appl. Math. 3 (1982), pp. 441-462. | MR | Zbl
and -[7] On Lommel and Bessel polynomials , Proc. Amer. Math. Soc. 5 (1954), pp. 946-956. | MR | Zbl
-[8] On a class of polynomials orthogonal over a denumerable set, Pacific J. Math. 6 (1956), pp. 239-247. | MR | Zbl
, and -[9] 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] Linear Operators, Part II: Spectral theory. Self Adjoint Operators in Hilbert Space, Interscience Publishers (John Wiley & Sons), New York, 1963. | MR | Zbl
and -[11] Orthogonal matrix polynomials and higher-order recurrence relations, Linear Algebra Appl. 219 (1995 ), pp. 261-280. | MR | Zbl
and -[12] On the asymptotics of the Tricomi-Carlitz polynomials and their zero distribution (I, SIAM J. Math. Anal. 25 ( 1994). pp. 420-428. | MR | Zbl
and -[13] Polynomials orthogonal over a denumerable set, Pacific J. Math. 15, n° 4 (1965), pp. 1171-1186. | MR | Zbl
-[14] 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] Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, 1966. | MR | Zbl
-[16] Orthogonal polynomials and Laurent polynomials related to the Hahn-Exton q-Bessel function , Constr. Approx. 11 (1995), pp. 477-512. | MR | Zbl
and -[17] 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.
and -[18] 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] A generalization of Poincaré's theorem for recurrence relations, J. Approx. Theory 63 (1990), pp. 92-97. | MR | Zbl
and -[20] 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
, and -[21] Orthogonal Polynomials, Memoirs Amer. Math. Soc. 213, Providence, RI, 1979. | MR | Zbl
-[22] Sur les équations linéaires aux différentielles et aux différences finies, Amer. J. Math. 7 (1885), pp. 203-258. | JFM | MR
-[23] A class of continued fractions, Duke Math. J. 6 (1940), pp. 48-65. | JFM | MR | Zbl
-[24] Convergence of continued fractions , Zap. Mat. Otod. Novoros. Obshchest. 8 (1888), pp. 97-127.
-[25] 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] Linear Transformations in Hilbert Space and their Applications to Analysis, Amer. Math. Soc. Colloq. Publ. 15, Providence, RI, 1932. | JFM | MR
-[27] 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] 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] 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] 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] On the convergence of algebraic continued fractions whose coefficients have limiting values, Trans. Amer. Math. Soc. 5 (1904 ), pp. 253-262. | JFM | MR
-[32] On continued fractions which represent meromorphic functions, Bull. Amer. Math. Soc. 39 (1933), pp. 946-952. | JFM | Zbl
-[33] On the continued fractions of the form K∞1(bνz/1, Bull. Amer. Math. Soc. 41 (1935), pp. 727-736. | Zbl
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