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Book Review
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Book Information
Author(s):
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:
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- 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.
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- 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
Additional Information:
Reviewer(s):
Joseph A.
Ball
Review Information:
Journal:
Bull. Amer. Math. Soc.
4
(1981),
357-362.
DOI:
10.1090/S0273-0979-1981-14915-6
PII:
S 0273-0979(1981)14915-6
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