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Book Review
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Book Information
Author(s):
T. Ya. Azizov and I. S. Iokhvidov
Title:
Linear operators in spaces with an indefinite metric
Additional book information:
John Wiley & Sons, 1989, 300 pp., $82.95. ISBN 0-471-92129-7
References:
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- [AI] T. Ya Azzizov and I. Iokhvidov, Linear operators in spaces with an indefinite metric, Mathematical Analysis 17 (Itogi nauki i tekhniki), 113-205, Moscow, 1979; (English Transl. J. Soviet Math. 15 (1981), 438-490. (Russian)
- [B] H. Bercovici, Review on Introduction to operator theory and invariant subspaces by Bernard Beauzamy, Bull, of Amer. Math. Soc. (N. S. ) 22 (1990), 148-152.
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- [BGR] J. A. Ball, I. Gohberg, and L. Rodman, Interpolation of rational matrix functions, OT45, Birkhäuser, 1990. MR 1083145
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- [Bo] J. Bognar, Indefinite inner product spaces, Springer-Verlag, Berlin, 1974. MR 467261
- [D] H. Dym, J-contractive matrix functions, reproducing kernel Hilbert spaces and interpolation, CBMS Regional Conf. Ser. in Math., vol. 71, Amer. Math. Soc. Providence, RI, 1989. MR 1004239
- [DK] Yu. L. Daletskiy and M. G. Krein, Stable solutions of differential equations in a Banach space (Russian), Nauka, Moscow, 1970; (English Transl.: Amer. Math. Soc. Transl. Math. Monographs, vol. 43, Providence, RI, 1974.
- [DL] K. Daho and H. Langer, Sturm-Liouville operators with an indefinite weight function, Proc. Royal Soc. Edinburgh 78A (1977), 161-191. MR 492490
- [Fr] B. Francis, A course in H∞ control theory, Lecture Notes in Control and Information Sciences, vol. 88, Springer-Verlag, Berlin and New York, 1987. MR 932459
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- [I] I. S. Iokhvidov, On a lemma of K. Fan generalizing A. N. Tikhonov's principle of fixed points, Dokl. Akad. Nauk USSR 159 (1964), 501-504. (Russian) MR 173158
- [IK] I. S. Iokhvidov and M. G. Krein, Spectral theory of operators in spaces with an indefinite metric. I (Russian), Trudy Moskov., Mat. Obsch. 5 (1965), 367-432; Amer. Math. Soc. Translations (2), 1960, 105-75; II (Russian), Trudy Moskov, Mat. Obshch, 8 (1969), 413-96; Amer. Math. Soc. Translations (2), 34, 283-373. MR 80879
- [IKL] I. S. Iokhvidov, M. G. Krein, and H. Langer, Introduction to the spectral theory of operators in spaces with an indefinite metric, Akademie-Verlag, Berlin, 1982. MR 691137
- [J] P. Jonas, On the functional calculus and the spectral function for definitizable operators in Krein space, Belträge Anal. 16 (1981), 121-135. MR 663475
- [K1] M. G. Krein, A new application of the fixed-point principle in the theory of linear operators in a space with an indefinite metric, Dokl. Akad. Nauk USSR 1964 154 (5) 1023-1026; (English Transl.: Soviet Math. Dokl. 5 (1964), 224-227. (Russian) MR 169059
- [K2] M. G. Krein, Introduction to the geometry of indefinite J-spaces and the theory of operators in those spaces, Second Summer Mathematical School, I, Kiev, 1965, 15-92; English Transl: AMS Transl. (2) 93 (1970), 103-176. (Russian) MR 192348
- [K] L. Kronecker, Ueber die congruenten Transformationen der bilinearen Formen, Monatsber. Akad. Wiss., Berlin, 1874, 397-447.
- [KL] M. G. Krein, and H. Langer, On some mathematical principles in the linear theory of damped oscillations of continua, Trudy mezhdunarod. simposiuma po prilozheniyam teorii funktsiy v mechanike sploshnoy sredy, vol. 2, Moscow, 1966, 283-322; (English transl.: Integral Equations and Operator Theory 1 (1978), 364-399; 539-566. MR 511976
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- [S] M. H. Stone, Linear transformations in Hilbert space and their applications to analysis, Amer. Math. Soc. Colloq. Publ., vol. 15, New York, 1932. MR 1451877
- [vN] J. von Neumann, Allgemeine Eigenwettheorie Hermitscher Funktionaloperatoren, Math. Ann. 102 (1929-1930), 49-131.
- [W] G. Wittstock, On invariant subspaces of positive transformations in spaces with indefinite metric, Math. Ann. 172 (1967), 167-175. (German)
- [We] K. Weierstrass, Zür Theorie der bilinearen und quadratischen Formen, Monatsber. Akad. Wiss., Berlin, 1868, pp. 310-338.
Additional Information:
Reviewer(s):
Leiba
Rodman
Review Information:
Journal:
Bull. Amer. Math. Soc.
25
(1991),
111-123.
DOI:
10.1090/S0273-0979-1991-16039-8
PII:
S 0273-0979(1991)16039-8
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