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Book Review

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Book Information:

Authors: Mikhail S. Livshits [Moshe Livsic] and Artem A. Yantsevich
Title: Operator colligations in Hilbert spaces
Additional book information: Winston, Washington, D. C. (distributed by Wiley, New York), 1979, xii + 212 pp., $19.95.

References [Enhancements On Off] (What's this?)

  • 1. V. M. Adamjan and D. Z. Arov, On unitary coupling of semiunitary operators, Amer. Math. Soc. Transl. (2) 95 (1970), 75-129. MR 206711
  • 2. P. R. Ahern and D. N. Clark, Invariant subspaces and analytic continuation in several variables, J. Math. Mech. 19 (1970), 963-969. MR 261340
  • 3. Harm Bart, Israel Gohberg, and Marinus A. Kaashoek, Minimal factorization of matrix and operator functions, Operator Theory: Advances and Applications, vol. 1, Birkhäuser Verlag, Basel-Boston, Mass., 1979. MR 560504
  • 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. MR 244795
  • 5. L. deBranges and J. Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York, 1966. MR 215065
  • 6. M. S. Brodskii, Triangular and Jordan representations of linear operators, Transl. Math. Mono., vol 32, Amer. Math. Soc., Providence, R. I., 1971. MR 322542
  • 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. MR 113144
  • 8. D. N. Clark, On commuting contractions, J. Math. Anal. Appl. 32 (1970), 590-596. MR 267407
  • 9. D. N. Clark, Some star-invariant subspaces in two variables, Duke Math. J. 39 (1972), 539-550. MR 353014
  • 10. D. N. Clark, Commutants that do not dilate, Proc. Amer. Math. Soc. 35 (1972), 483-486. MR 303313
  • 11. H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 171178
  • 12. J. W. Helton, The characteristic functions of operator theory and electrical network realization, Indiana Univ. Math. J. 22 (1972), 403-414. MR 306951
  • 13. J. W. Helton, Discrete time systems, operator models, and scattering theory, J. Functional Analysis 16 (1974), 15-38. MR 445310
  • 14. J. William Helton, The distance of a function to 𝐻^{∞} in the Poincaré metric; electrical power transfer, J. Funct. Anal. 38 (1980), no. 2, 273–314. MR 587910, https://doi.org/10.1016/0022-1236(80)90066-X
  • 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. MR 433235
  • 17. P. Lax and R. S. Phillips, Scattering theory, Academic Press, New York, 1967. MR 217440
  • 18. M. S. Livsic, On the spectral decomposition of linear non-self-adjoint operators, Amer. Math. Soc. Transl. (2) 5 (1957), 67-114. MR 83703
  • 19. M. S. Livsic, Operators, oscillations, waves and open systems, Transl. Math. Mono., vol. 34, Amer. Math. Soc., Providence, R. I., 1973. MR 347396
  • 20. M. S. Livšic, Operator waves in Hilbert space and related partial differential equations, Integral Equations Operator Theory 2 (1979), no. 1, 25–47. MR 532737, https://doi.org/10.1007/BF01729359
  • 21. M. S. Livšic, A method for constructing triangular canonical models of commuting operators based on connections with algebraic curves, Integral Equations Operator Theory 3 (1980), no. 4, 489–507. MR 595748, https://doi.org/10.1007/BF01702312
  • 22. B. Sz.-Nagy and C. Foias, Harmonic analysis of operators on Hilbert space, American Elsevier, New York, 1970. MR 275190
  • 23. W. Rudin, Function theory in polydisks, Benjamin, New York, 1969. MR 255841

Review Information:

Reviewer: Joseph A. Ball
Journal: Bull. Amer. Math. Soc. 4 (1981), 357-362
DOI: https://doi.org/10.1090/S0273-0979-1981-14915-6
American Mathematical Society