Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF
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, Unitary couplings of semi-unitary operators, Mat. Issled. 1 (1966), no. vyp. 2, 3–64 (Russian). MR 0206711
  • 2. P. R. Ahern and D. N. Clark, Invariant subspaces and analytic continuation in several variables., J. Math. Mech. 19 (1969/1970), 963–969. MR 0261340
  • 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. Louis de Branges and James Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965) Wiley, New York, 1966, pp. 295–392. MR 0244795
  • 5. Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065
  • 6. M. S. Brodskiĭ, Triangular and Jordan representations of linear operators, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin; Translations of Mathematical Monographs, Vol. 32. MR 0322542
  • 7. M. S. Brodskiĭ and M. S. Livšic, Spectral analysis of non-selfadjoint operators and intermediate systems, Amer. Math. Soc. Transl. (2) 13 (1960), 265–346. MR 0113144
  • 8. Douglas N. Clark, On commuting contractions, J. Math. Anal. Appl. 32 (1970), 590–596. MR 0267407
  • 9. Douglas N. Clark, Some star-invariant subspaces in two variables, Duke Math. J. 39 (1972), 539–550. MR 0353014
  • 10. Douglas N. Clark, Commutants that do not dilate, Proc. Amer. Math. Soc. 35 (1972), 483–486. MR 0303313, 10.1090/S0002-9939-1972-0303313-X
  • 11. Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
  • 12. J. William Helton, The characteristic functions of operator theory and electrical network realization, Indiana Univ. Math. J. 22 (1972/73), 403–414. MR 0306951
  • 13. J. William Helton, Discrete time systems, operator models, and scattering theory, J. Functional Analysis 16 (1974), 15–38. MR 0445310
  • 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, 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. Thomas L. Kriete, Canonical models and the self-adjoint parts of dissipative operators, J. Functional Analysis 23 (1976), no. 1, 39–94. MR 0433235
  • 17. Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
  • 18. M. S. Lovšic, On the spectral resolution of linear non-selfadjoint operators, Amer. Math. Soc. Transl. (2) 5 (1957), 67–114. MR 0083703
  • 19. M. S. Livšic, Operators, oscillations, waves (open systems), American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by Scripta Technica, Ltd. English translation edited by R. Herden; Translations of Mathematical Monographs, Vol. 34. MR 0347396
  • 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, 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, 10.1007/BF01702312
  • 22. Béla Sz.-Nagy and Ciprian Foiaș, Harmonic analysis of operators on Hilbert space, Translated from the French and revised, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. MR 0275190
  • 23. Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841

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