Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

The factorization problem for nonnegative operator valued functions


Authors: Marvin Rosenblum and James Rovnyak
Journal: Bull. Amer. Math. Soc. 77 (1971), 287-318
MSC (1970): Primary 47B35; Secondary 30A78, 46E40, 60G25
DOI: https://doi.org/10.1090/S0002-9904-1971-12671-X
MathSciNet review: 0273437
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. N. I. Ahiezer, On the theory of entire functions of finite degree, Dokl. Akad. Nauk SSSR 63 (1948), 475-478. (Russian) MR 10, 289. MR 27333
  • 2. R. P. Boas, Jr, Entire functions. Academic Press, New York, 1954. MR 16, 914. MR 68627
  • 3. L. de Branges, Hilbert spaces of entire functions, Prentice-Hall, Englewood Cliffs, New Jersey, 1968. MR 37 #4590. MR 229011
  • 4. L. de Branges and J. Rovnyak, "Appendix on square summable power series, " in, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics, Wiley, New York, 1966, pp. 347-392. MR 244795
  • 5. A. Brown and P. R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/64), 89-102. MR 28 #3350; MR 30 p. 1205. MR 160136
  • 6. A. Devinatz, The factorization of operator valued functions, Ann. of Math. (2) 73 (1961), 458-495. MR 23 #A3997. MR 126702
  • 7. R. G. Douglas, On factoring positive operator functions, J. Math. Mech. 16 (1966), 119-126. MR 35 #782. MR 209887
  • 8. L. Gårding and L. Hörmander, Strongly subharmonic functions, Math. Scand. 15 (1964), 93-96. MR 31 #3621. MR 179373
  • 9. I. C. Gohberg, The factorization problem for operator functions, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1055-1082; English transl., Amer. Math. Soc. Transl. (2) 49 (1966), 130-161. MR 30 #5182. MR 174994
  • 10. H. Helson, Lectures on invariant subspaces, Academic Press, New York, 1964. MR 30 #1409. MR 171178
  • 11. H. Helson and D. Lowdenslager, Prediction theory and Fourier series in several variables, Acta Math. 99 (1958), 165-202; II, ibid. 106 (1961), 175-213. MR 20 #4155; MR 31 #562. MR 97688
  • 12. K. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Series in Modern Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962. MR 24 #A2844. MR 133008
  • 13. M. G. Kreĭn, A contribution to the theory of entire functions of exponential type, Izv. Akad. Nauk SSSR 11 (1947), 309-326. (Russian) MR 9, 179. MR 22252
  • 14. T. L. Kriete, A generalized Paley- Wiener theorem, J. Math. Anal. Appl. (to appear). MR 288275
  • 15. P. D. Lax, Translation invariant spaces, Proc. Internat. Sympos. on Linear Spaces (Jerusalem, 1960), Jerusalem Academic Press, Jerusalem; Pergamon Press, Oxford, 1961. MR 25 #4345. MR 140931
  • 16. B. Ja. Levin, Distribution of zeros of entire functions, GITTL, Moscow, 1956; English transl., Transl. Math. Monographs, vol. 5, Amer. Math. Soc. Providence, R. I., 1964. MR 19, 402; MR 28 #217. MR 156975
  • 17. D. Lowdenslager, On factoring matrix valued functions, Ann. of Math. (2) 78 (1963), 450-454. MR 27 #6094. MR 155154
  • 18. P. Masani, Shift invariant spaces and prediction theory, Acta Math. 107 (1962), 275-290. MR 25 #4344. MR 140930
  • 19. B. Moore, Outer factorization for vectorial Toeplitz operators, Dissertation, University of Virginia, Charlottesville, Va., 1969.
  • 20. B. Moore, The Szegö infimum, Proc. Amer. Math. Soc. 29 (1971), (to appear). MR 290170
  • 21. B. Sz.-Nagy and C. Foias, Analyse harmonique des operáteurs de l'espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967. MR 37 #877.
  • 22. I. I. Privalov, Boundary properties of analytic functions, GITTL, Moscow, 1950; German transl., Hochschulbücher für Math., Band 25, VEB Deutscher Verlag, Berlin, 1956. MR 13, 926; MR 18, 727. MR 47765
  • 23. E. A. Robinson, Extremal representation of stationary stochastic processes, Ark. Mat. 4 (1962), 379-384. MR 25 #4576. MR 141165
  • 24. M. Rosenblatt, A multi-dimensional prediction problem, Ark. Mat. 3 (1958), 407-424. MR 19, 1098. MR 92332
  • 25. M. Rosenblum, Vectorial Toeplitz operators and the Fejér-Riesz theorem, J. Math. Anal. Appl. 23 (1968), 139-147. MR 37 #3378. MR 227794
  • 26. M. Rosenblum and J. Rovnyak, Factorization of operator valued entire functions, Indiana Univ. Math. J. 20 (1970), 157-173. MR 261390
  • 27. Ju A. Rozanov, Stationary random processes, Fizmatgiz, Moscow, 1963; English transl., Holden-Day, San Francisco, Calif., 1967. MR 28 #2580; MR 35 #4985. MR 214134
  • 28. N. Wiener and P. Masani, The prediction theory of multivariate stochastic processes. I., The regularity condition, Acta Math. 98 (1957), 111-150; II. The linear predictor, ibid., 99 (1958), 93-137. MR 20 #4323; MR 20 #4325. MR 97856

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 47B35, 30A78, 46E40, 60G25

Retrieve articles in all journals with MSC (1970): 47B35, 30A78, 46E40, 60G25


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1971-12671-X

American Mathematical Society