Book Review
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MathSciNet review:
1567320
Full text of 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.
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
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
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
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
Louis de Branges and James Rovnyak, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065
M. S. Brodskiĭ, 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
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
Douglas N. Clark, On commuting contractions, J. Math. Anal. Appl. 32 (1970), 590–596. MR 267407, DOI 10.1016/0022-247X(70)90281-7
Douglas N. Clark, Some star-invariant subspaces in two variables, Duke Math. J. 39 (1972), 539–550. MR 353014
Douglas N. Clark, Commutants that do not dilate, Proc. Amer. Math. Soc. 35 (1972), 483–486. MR 303313, DOI 10.1090/S0002-9939-1972-0303313-X
Henry Helson, Lectures on invariant subspaces, Academic Press, New York-London, 1964. MR 0171178
J. William Helton, 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
J. William Helton, 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
J. William Helton, 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. N. Kravitsky, On the discriminant function of two commuting nonself-adjoint operators, Math. Report No. 223, Ben Gurion Univ., Israel, 1979.
Thomas L. Kriete, 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
Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
M. S. Lovšic, On the spectral resolution of linear non-selfadjoint operators, Amer. Math. Soc. Transl. (2) 5 (1957), 67–114. MR 0083703
M. S. Livšic, 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
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, DOI 10.1007/BF01729359
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, DOI 10.1007/BF01702312
Béla Sz.-Nagy and Ciprian Foiaş, 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
Walter Rudin, Function theory in polydiscs, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0255841
- 1.
- V. M. Adamjan and D. Z. Arov, On unitary coupling of semiunitary operators, Amer. Math. Soc. Transl. (2) 95 (1970), 75-129. MR 0206711
- 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.
- H. Bart, I. Gohberg and M. A. Kaashoek, Minimal factorization of matrix and operator functions, Birkhäuser Verlag, Basel, 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. W. Helton, The distance of a function to H; electric power transfer, J. Functional Analysis (to appear). MR 587910
- 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. Livsic, Operator waves in Hilbert space and related partial differential equations, Integral Equations Operator Theory 2 (1979), 25-47. MR 532737
- 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. MR 595748
- 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
