Book Review

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

MathSciNet review: 1567320

Full text of review: PDF This review is available free of charge.

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.

*Unitary couplings of semi-unitary operators*, Mat. Issled.

**1**(1966), no. vyp. 2, 3–64 (Russian). MR

**0206711**

*Invariant subspaces and analytic continuation in several variables.*, J. Math. Mech.

**19**(1969/1970), 963–969. MR

**0261340**

*Minimal factorization of matrix and operator functions*, Operator Theory: Advances and Applications, vol. 1, Birkhäuser Verlag, Basel-Boston, Mass., 1979. MR

**560504**

*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**

*Square summable power series*, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR

**0215065**

*Triangular and Jordan representations of linear operators*, Translations of Mathematical Monographs, Vol. 32, American Mathematical Society, Providence, R.I., 1971. Translated from the Russian by J. M. Danskin. MR

**0322542**

*Spectral analysis of non-selfadjoint operators and intermediate systems*, Amer. Math. Soc. Transl. (2)

**13**(1960), 265–346. MR

**0113144**

*On commuting contractions*, J. Math. Anal. Appl.

**32**(1970), 590–596. MR

**267407**, DOI 10.1016/0022-247X(70)90281-7

*Some star-invariant subspaces in two variables*, Duke Math. J.

**39**(1972), 539–550. MR

**353014**

*Commutants that do not dilate*, Proc. Amer. Math. Soc.

**35**(1972), 483–486. MR

**303313**, DOI 10.1090/S0002-9939-1972-0303313-X

*Lectures on invariant subspaces*, Academic Press, New York-London, 1964. MR

**0171178**

*The characteristic functions of operator theory and electrical network realization*, Indiana Univ. Math. J.

**22**(1972/73), 403–414. MR

**306951**, DOI 10.1512/iumj.1972.22.22035

*Discrete time systems, operator models, and scattering theory*, J. Functional Analysis

**16**(1974), 15–38. MR

**0445310**, DOI 10.1016/0022-1236(74)90069-x

*The distance of a function to $H^{\infty }$ in the Poincaré metric; electrical power transfer*, J. Functional Analysis

**38**(1980), no. 2, 273–314. MR

**587910**, DOI 10.1016/0022-1236(80)90066-X

**15.**

*On the discriminant function of two commuting nonself-adjoint operators*, Math. Report No. 223, Ben Gurion Univ., Israel, 1979.

*Canonical models and the self-adjoint parts of dissipative operators*, J. Functional Analysis

**23**(1976), no. 1, 39–94. MR

**0433235**, DOI 10.1016/0022-1236(76)90058-6

*Scattering theory*, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR

**0217440**

*On the spectral resolution of linear non-selfadjoint operators*, Amer. Math. Soc. Transl. (2)

**5**(1957), 67–114. MR

**0083703**

*Operators, oscillations, waves (open systems)*, Translations of Mathematical Monographs, Vol. 34, American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by Scripta Technica, Ltd. English translation edited by R. Herden. MR

**0347396**

*Operator waves in Hilbert space and related partial differential equations*, Integral Equations Operator Theory

**2**(1979), no. 1, 25–47. MR

**532737**, DOI 10.1007/BF01729359

*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**, DOI 10.1007/BF01702312

*Harmonic analysis of operators on Hilbert space*, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970. Translated from the French and revised. MR

**0275190**

*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