Book Review
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MathSciNet review:
1567021
Full text of review:
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Book Information:
Author:
A. V. Balakrishnan
Title:
Applied functional analysis
Additional book information:
Springer-Verlag, New York, Heidelberg, Berlin, 1976, vii + 309 pp., $19.80.
David J. Aldous, A characterisation of Hilbert space using the central limit theorem, J. London Math. Soc. (2) 14 (1976), no. 2, 376–380. MR 443017, DOI 10.1112/jlms/s2-14.2.376
Karl J. Ȧström, Introduction to stochastic control theory, Mathematics in Science and Engineering, Vol. 70, Academic Press, New York-London, 1970. MR 0270799
3. M. Athans, Towards a practical theory for distributed parameter Systems, IEEE Trans. Automatic Control, AC-15 (1970), 245-247.
A. V. Balakrishnan, Introduction to optimization theory in a Hilbert space, Lecture Notes in Operations Research and Mathematical Systems, Vol. 42, Springer-Verlag, Berlin-New York, 1971. MR 0282278
5. A. Bensoussan, Filtrage optimal des systèmes linéaires, Dunod, Paris, 1971.
6. R. Brockett, Finite dimensional linear systems, Wiley, New York, 1970.
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
Richard S. Bucy and Peter D. Joseph, Filtering for stochastic processes with applications to guidance, Interscience Tracts in Pure and Applied Mathematics, No. 23, Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR 0267946
Ruth Curtain, A survey of infinite-dimensional filtering, SIAM Rev. 17 (1975), 395–411. MR 406638, DOI 10.1137/1017041
Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745
Peter L. Falb, Infinite-dimensional filtering: The Kalman-Bucy filter in Hilbert space, Information and Control 11 (1967), 102–137. MR 226958
J. William Helton, Systems with infinite-dimensional state space: the Hilbert space approach, Proc. IEEE 64 (1976), no. 1, 145–160. Recent trends in system theory. MR 0416694
13. A. Jazwinski, Stochastic processes and filtering theory, Academic Press, New York, 1970.
Thomas Kailath, A view of three decades of linear filtering theory, IEEE Trans. Inform. Theory IT-20 (1974), 146–181. MR 465437, DOI 10.1109/tit.1974.1055174
J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263–269. MR 276734, DOI 10.1007/BF02771592
Krzysztof Maurin, Methods of Hilbert spaces, Monografie Matematyczne, Tom 45, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. Translated from the Polish by Andrzej Alexiewicz and Waclaw Zawadowski. MR 0223910
17. T. McGarty, Stochastic systems and state estimation, Interscience, New York, 1974.
Topics in operator theory, Mathematical Surveys, No. 13, American Mathematical Society, Providence, R.I., 1974. Edited by C. Pearcy. MR 0350446
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
- 1.
- D. Aldous, A characterization of Hilbert space using the central limit theorem, J. London Math. Soc. 14 (1976), 376-380. MR 0443017
- 2.
- K. Aström, Introduction to stochastic control theory, Academic Press, New York, 1970. MR 270799
- 3.
- M. Athans, Towards a practical theory for distributed parameter Systems, IEEE Trans. Automatic Control, AC-15 (1970), 245-247.
- 4.
- A. Balakrishnan, Introduction to optimization theory in a Hilbert space, Lecture Notes in Econ. and Math. Systems no. 42, Springer-Verlag, Berlin and New York, 1971. MR 282278
- 5.
- A. Bensoussan, Filtrage optimal des systèmes linéaires, Dunod, Paris, 1971.
- 6.
- R. Brockett, Finite dimensional linear systems, Wiley, New York, 1970.
- 7.
- M. Brodskiĭ, Triangular and Jordan representations of linear operators. Transl. Math. Monographs, no. 32, Amer. Math. Soc., Providence, R. I., 1972. MR 322542
- 8.
- R. Bucy and P. Joseph, Filtering for stochastic processes with applications to guidance, Wiley, New York, 1968. MR 267946
- 9.
- R. Curtain, A survey of infinite dimensional filtering, SIAM Review 17 (1975), 395-411. MR 406638
- 10.
- N. Dunford and J. Schwartz, Linear operators (Part II: Spectral theory), Interscience, New York, 1963. MR 188745
- 11.
- P. Falb, Infinite dimensional filtering, Information and Control 11 (1967), 102-137. MR 226958
- 12.
- W. Helton, Systems with infinite dimensional state space: The Hilbert space approach, Proc. IEEE 64 (1976), 145-159. MR 416694
- 13.
- A. Jazwinski, Stochastic processes and filtering theory, Academic Press, New York, 1970.
- 14.
- T. Kailath, A view of three decades of linear filtering theory, IEEE Trans. Information Theory, IT-20 (1974), 145-181. MR 465437
- 15.
- J. Lindenstrauss and L. Tzafriri, On the complemented subspaces problem, Israel J. Math. 9 (1971), 263-269. MR 276734
- 16.
- K. Maurin, Methods of Hilbert spaces, Polish Scientific Publishers, Warsaw, 1967. MR 223910
- 17.
- T. McGarty, Stochastic systems and state estimation, Interscience, New York, 1974.
- 18.
- C. Pearcy (Editor), Topics in operator theory, Math. Surveys, no. 13, Amer. Math. Soc., Providence, R. I., 1974. MR 350446
- 19.
- B. Sz.-Nagy and C. Foiaş, Harmonic analysis of operators on Hilbert space, North-Holland, Amsterdam, 1970. MR 275190
Review Information:
Reviewer:
Richard B. Holmes
Journal:
Bull. Amer. Math. Soc.
84 (1978), 65-71
DOI:
https://doi.org/10.1090/S0002-9904-1978-14408-5
