Bulletin (New Series) of the American Mathematical Society

Review: Mikhail S. Livshits [Moshe Livsic] and Artem A. Yantsevich, Operator colligations in Hilbert spaces

Joseph A. Ball

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.) Volume 4, Number 3 (1981), 357-362.

First available in Project Euclid: 4 July 2007

Permanent link to this document


Ball, Joseph A. Review: Mikhail S. Livshits [Moshe Livsic] and Artem A. Yantsevich, Operator colligations in Hilbert spaces. Bull. Amer. Math. Soc. (N.S.) 4 (1981), no. 3, 357--362.https://projecteuclid.org/euclid.bams/1183548128

Export citation


  • 1. V. M. Adamjan and D. Z. Arov, On unitary coupling of semiunitary operators, Amer. Math. Soc. Transl. (2) 95 (1970), 75-129.
  • 2. P. R. Ahern and D. N. Clark, Invariant subspaces and analytic continuation in several variables, J. Math. Mech. 19 (1970), 963-969.
  • 3. H. Bart, I. Gohberg and M. A. Kaashoek, Minimal factorization of matrix and operator functions, Birkhäuser Verlag, Basel, 1979.
  • 4. L. deBranges and J. Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Application in Quantum Mechanics (Calvin H. Wilcox, ed.), Wiley, New York, 1966.
  • 5. L. deBranges and J. Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York, 1966.
  • 6. M. S. Brodskii, Triangular and Jordan representations of linear operators, Transl. Math. Mono., vol 32, Amer. Math. Soc., Providence, R. I., 1971.
  • 7. M. S. Brodskii and M. S. Livsic, Spectral analysis of non-self-adjoint operators and intermediate systems, Amer. Math. Soc. Transl. (2) 13 (1960), 265-346.
  • 8. D. N. Clark, On commuting contractions, J. Math. Anal. Appl. 32 (1970), 590-596.
  • 9. D. N. Clark, Some star-invariant subspaces in two variables, Duke Math. J. 39 (1972), 539-550.
  • 10. D. N. Clark, Commutants that do not dilate, Proc. Amer. Math. Soc. 35 (1972), 483-486.
  • 11. H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964.
  • 12. J. W. Helton, The characteristic functions of operator theory and electrical network realization, Indiana Univ. Math. J. 22 (1972), 403-414.
  • 13. J. W. Helton, Discrete time systems, operator models, and scattering theory, J. Functional Analysis 16 (1974), 15-38.
  • 14. J. W. Helton, The distance of a function to H in the Poincaré metric; electric power transfer, J. Functional Analysis (to appear).
  • 15. N. Kravitsky, On the discriminant function of two commuting nonself-adjoint operators, Math. Report No. 223, Ben Gurion Univ., Israel, 1979.
  • 16. T. L. Kriete, Canonical modesl and the self-adjoint parts of dissipative operators, J. Functional Analysis 23 (1976), 39-94.
  • 17. P. Lax and R. S. Phillips, Scattering theory, Academic Press, New York, 1967.
  • 18. M. S. Livsic, On the spectral decomposition of linear non-self-adjoint operators, Amer. Math. Soc. Transl. (2) 5 (1957), 67-114.
  • 19. M. S. Livsic, Operators, oscillations, waves and open systems, Transl. Math. Mono., vol. 34, Amer. Math. Soc., Providence, R. I., 1973.
  • 20. M. S. Livsic, Operator waves in Hilbert space and related partial differential equations, Integral Equations Operator Theory 2 (1979), 25-47.
  • 21. M. S. Livsic, A method for constructing triangular canonical models of commuting operators based on connections with algebraic curves, Math. Report No. 231, Ben Gurion Univ., Israel, 1980.
  • 22. B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, American Elsevier, New York, 1970.
  • 23. W. Rudin, Function theory in polydisks, Benjamin, New York, 1969.