Weakly Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization Periodic Sequences of Bounded Linear Transformations: A Spectral Characterization

Georgian Mathematical Journal

Volumn 6, Issue 1, 1999, Pages 91-98

  Soltani, A R ^a   Shishebor, Z ^b  

^a INSTITUTE FOR STUDIES IN THEORETICAL PHYSICS AND MATHEMATICS IPM   (Iran)

^b SHIRAZ UNIVERSITY   (Iran)

Author keywords

Bounded linear operators; Hilbert space; Spectral representation; Weakly periodic sequences

Indexed keywords

EID: 85012815043     PISSN: 1072947X     EISSN: 15729176     Source Type: Journal    
DOI: 10.1515/GMJ.1999.91     Document Type: Article

References (11)

1. H. L. Hurd and V. Mandrekar, Spectral theory of periodically and quasi-periodically stationary SaS sequences. Tech. Report No. 349, Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, AC27599-AC33260, USA, 1991.
2. E. G. Gladyshev, Periodically correlated random sequences. Soviet Math. Dokl. 2(1961), 385-388.
3. A. G. Miamee, Periodically correlated processes and their stationary dilations. SIAM J. Appl. Math. 50(1990), 1194-1199.
4. M. Pourahmadi and H. Salehi, On subordination and linear transformation of harmonizable and periodically correlated processes. Probability Theory on Vector Spaces, III (Lublin), Lecture Notes in Math., 1080, 195-213, Springer, Berlin-New York, 1983.
5. Yu. A. Rozanov, Some approximation problems in the theory of stationary processes. J. Multivariate Anal. 2(1972), 135-144.
6. Z. Shishebor and A. R. Soltani, A spectral representation weakly periodic sequences of bounded linear transformations. Technical report, Department of Statistics, Shiraz University, Shiraz, Iran, 1995.
7. V. Mandrekar and H. Salehi, On singularity and Lebesgue type decomposition for operator-valued measures. J. Multivariate Anal. 2(1971), 167-185.
8. N. Dunford and J. T. Schwartz, Linear operators, I. Interscience, New York, 1958.
9. J. Diestel and J. J. Uhl, Vector measures. Amer. Math. Soc., Providence, R.I., 1977.
10. Yu. A. Rozanov, Stationary random processes. Holden-Day, San Francisco, 1967.
11. G. T. Adams, P. J. McGuire, and V. I. Paulsen, Analytic reproducing kernels and multiplication operators. Illinois J. Math. 36(1992), 404-419.