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Author: M. Bakonyi and T. Constantinescu
Title: Schur's algorithm and several applications
Additional book information: Pitman Research Notes in Mathematics Series, volume 261, Longman Scientific and Technical, \!Harlow, \!1992, \!1\!90 pp., \!US$54.95. \!ISBN 0-582-90120-9 Copublished in the U. S. by John Wiley \& Sons. ISBN 0-470-21974-2.

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V. M. Adamjan, D. Z. Arov, and M. G. Kreĭn, Infinite Hankel matrices and generalized Carathéodory-Fejér and I. Schur problems, Funkcional. Anal. i Priložen. 2 (1968), no. 4, 1–17 (Russian). MR 0636333

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D. Z. Arov, The influence of V. P. Potapov and M. G. Kreĭn on my scientific work, Matrix and operator valued functions, Oper. Theory Adv. Appl., vol. 72, Birkhäuser, Basel, 1994, pp. 1–16. MR 1310357

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Joseph A. Ball, Israel Gohberg, and Leiba Rodman, Interpolation of rational matrix functions, Operator Theory: Advances and Applications, vol. 45, Birkhäuser Verlag, Basel, 1990. MR 1083145, DOI 10.1007/978-3-0348-7709-1

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T. Constantinescu, On the structure of positive Toeplitz forms, Dilation theory, Toeplitz operators, and other topics (Timişoara/Herculane, 1982) Oper. Theory Adv. Appl., vol. 11, Birkhäuser, Basel, 1983, pp. 127–149. MR 789634

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T. Constantinescu, An algorithm for the operatorial Carathéodory-Fejér problem, Spectral theory of linear operators and related topics (Timişoara/Herculane, 1983) Oper. Theory Adv. Appl., vol. 14, Birkhäuser, Basel, 1984, pp. 81–107. MR 789610

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P. Delsarte and Y. Genin, On the role of orthogonal polynomials on the unit circle in digital signal processing applications, Orthogonal polynomials (Columbus, OH, 1989) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 294, Kluwer Acad. Publ., Dordrecht, 1990, pp. 115–133. MR 1100290

Patrick Dewilde and Harry Dym, Lossless chain scattering matrices and optimum linear prediction: the vector case, Internat. J. Circuit Theory Appl. 9 (1981), no. 2, 135–175. MR 612268, DOI 10.1002/cta.4490090203

Vladimir K. Dubovoj, Bernd Fritzsche, and Bernd Kirstein, Matricial version of the classical Schur problem, Teubner-Texte zur Mathematik [Teubner Texts in Mathematics], vol. 129, B. G. Teubner Verlagsgesellschaft mbH, Stuttgart, 1992. With German, French and Russian summaries. MR 1152328

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Ciprian Foias and Arthur E. Frazho, The commutant lifting approach to interpolation problems, Operator Theory: Advances and Applications, vol. 44, Birkhäuser Verlag, Basel, 1990. MR 1120546, DOI 10.1007/978-3-0348-7712-1

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J. Geronimus, On polynomials orthogonal on the circle, on trigonometric moment-problem and on allied Carathéodory and Schur functions, Rec. Math. [Mat. Sbornik] N. S. 15(57) (1944), 99–130 (Russian., with English summary). MR 0012715

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J. William Helton, Joseph A. Ball, Charles R. Johnson, and John N. Palmer, Operator theory, analytic functions, matrices, and electrical engineering, CBMS Regional Conference Series in Mathematics, vol. 68, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1987. MR 896034, DOI 10.1090/cbms/068

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I. V. Kovalishina and V. P. Potapov, Integral representation of Hermitian positive functions, T. Ando, Hokkaido University, Sapporo, 1982. Translated from the Russian by T. Ando. MR 711021

M. G. Kreĭn and A. A. Nudel′man, The Markov moment problem and extremal problems, Translations of Mathematical Monographs, Vol. 50, American Mathematical Society, Providence, R.I., 1977. Ideas and problems of P. L. Čebyšev and A. A. Markov and their further development; Translated from the Russian by D. Louvish. MR 0458081

Xian-Jin Li, Hilbert spaces of entire functions and polynomials orthogonal on the unit circle, Methods Appl. Anal. 1 (1994), no. 1, 25–43. MR 1260381, DOI 10.4310/MAA.1994.v1.n1.a3

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I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind. I, II, J. Reine Angew. Math. 147 (1917), 205-232; 148 (1918), 122-145; Gesammelte Abhandlungen, Vol. II, nos. 29, 30; reprinted in Herglotz, Schur, et al. [22]; English translation in Gohberg [20].

G. Szegő, Beiträge zur Theorie der Toeplitzschen Formen, Math. Z. 6 (1920), no. 3-4, 167–202 (German). MR 1544404, DOI 10.1007/BF01199955

G. Szegö, Concerning sets of polynomials orthogonal simultaneously on several circles, Bull. Amer. Math. Soc. 45 (1939), no. 2, 129–132. MR 1563925, DOI 10.1090/S0002-9904-1939-06915-2

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V. M. Adamjan, D. Z. Arov, and M. G. Kreĭn, Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and F. Riesz, Functional Anal. Appl. 2 (1968), 1-18. MR 0234274 (38:2591)

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-, Infinite Hankel matrices and generalized Carathéodory-Fejér and I. Schur problems, Functional Anal. Appl. 2 (1968), 269-281. MR 0636333 (58:30446)

[3]

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Z. Ceauşescu and C. Foiaş, On intertwining dilations. V, Acta Sci. Math. (Szeged) 40 (1978), 9-32. MR 496820 (82d:47013b)

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T. Constantinescu, On the structure of positive Toeplitz forms, Oper. Theory Adv. Appl., vol. 11, Birkhäuser, Basel and Boston, 1983, pp. 127-149. MR 789634 (86h:47033)

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-, On the structure of the Naimark dilation, J. Operator Theory 12 (1984), 159-175. MR 757117 (86b:47044)

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P. Delsarte and Y. Genin, On the role of orthogonal polynomials on the unit circle in digital signal processing applications, Orthogonal Polynomials: Theory and Practice (Columbus, OH, 1989), Kluwer, Dordrecht, 1990, pp. 115-133. MR 1100290 (92b:94002)

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V. K. Dubovoj, B. Fritzsche, and B. Kirstein, Matricial version of the classical Schur problem, Teubner-Texte, bd. 129, B. G. Teubner, Verlagsgesellschaft, Stuttgart, 1992. MR 1152328 (93e:47021)

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H. Dym, J contractive matrix functions, reproducing kernel Hilbert spaces, and interpolation, CBMS Reg. Conf. Ser. Math., vol. 71, Amer. Math. Soc., Providence, RI, 1989. MR 1004239 (90g:47003)

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C. Foiaş. and A. Frazho, The commutant lifting approach to interpolation problems, Oper. Theory Adv. Appl., vol. 44, Birkhäuser, Basel and Boston, 1990. MR 1120546 (92k:47033)

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J. Geronimus, On polynomials orthogonal on the circle, on trigonometric moment-problem and on allied Carathéodory and Schur functions, C. R. (Doklady) Acad. Sci. USSR (N.S.) 39 (1943), 291-295. MR 0010739 (6:62g)

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I. Gohberg, ed., I. Schur methods in operator theory and signal processing, Oper. Theory Adv. Appl., vol. 18, Birkhäuser, Basel and Boston, 1986.

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