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Các phân rã kiểu Wold cho một cặp bán nhóm đồng cấu không giao hoán của các ánh xạ đồng nhất
Tóm tắt
Trong bài báo này, một cặp bán nhóm đồng cấu không giao hoán trên không gian Hilbert được xem xét. Việc tồn tại và tính duy nhất của các phân rã kiểu Wold cho cặp này được nghiên cứu và có những liên kết với phân rã Wold không giao hoán cho bán nhóm tích sinh bởi cặp này. Ngoài ra, các điều kiện để bán nhóm tích trở thành một bán nhóm chuẩn cũng được trình bày.
Từ khóa
#bán nhóm đồng cấu #không gian Hilbert #phân rã Wold #bán nhóm chuẩnTài liệu tham khảo
Burdak, Z., Kosiek, M., Słociński, M.: The canonical Wold decomposition of commuting isometries with finite dimensional wandering spaces. Bull. Sci. Math. 137, 653–658 (2013)
Burdak, Z., Kosiek, M., Pagacz, P., Słociński, M.: Shift-type properties of commuting, completely non doubly commuting pairs of isometries. Integral Equ. Oper. Theory 79(1), 107–122 (2014)
Francos, J.M., Narasimhan, A., Woods, W.: Maximum-likelihood parameter estimation of the harmonic, evanescent and purely indeterministic components of discrete homogeneous random fields. IEEE Trans. Inf. Theory 42(3), 916–930 (1996)
Frazho, A.E.: Complements to models for noncommuting operators. J. Funct. Anal. 59, 445–461 (1984)
Gaşpar, D., Suciu, N.: On Wold decompositions of isometric semigroups. In: Butzer, P.L., Stens, R.L., Nagy, B.S. (eds.) Approximation Theory and Functional Analysis, vol. ISNM 65, pp. 99–108. Birkhauser Verlag, Basel (1984)
Gaşpar, D., Suciu, N.: Intertwining properties of isometric semigroups and Wold type decompositions. Operator Theory: Adv. Appl. 24, 183–193 (1987)
Gaşpar, D., Suciu, N.: Wold decompositions for commutative families of isometries. An. Univ. Timisoara Ser. Stiint. Mat. 27, 31–38 (1989)
Găvruţă, P., Bînzar, T.: Wold decompositions of the isometric semigroups. In: Proceedings of the National Conference on Mathematical Analysia and Applicatons, pp. 101–110. Timişoara (2000)
Helson, H., Lowdenslager, D.: Prediction theory and Fourier series in several variables. II. Acta Math. 106, 175–213 (1961)
Kallianpur, G., Mandrekar, V.: Nondeterministic random fields and Wold and Halmos decompositions for commuting isometries. In: Mandrekar, V., Salehi, H. (eds.) Prediction Theory and Harmonic Analysis, pp. 165–190. North-Holland, Amsterdam (1983)
Liu, F., Picard, R.W.: A spectral 2-D Wold decomposition algorithm for homogeneous random fields. In: ICASSP 99, vol. 4, pp. 3501–3504 (1999)
Muhly, P.S.: A structure theory for isometric representations of a class of semigroups. J. Reine Angew. Math. 225, 135–154 (1972)
Pater, F., Lemle, L.D., Bînzar, T.: On a Wold-Słociński’s type decomposition of a pair of commuting semigroups of isometries. In: ICNAAM, pp. 1379–1381 (2010)
Popescu, G.: Isometric dilations for infinite sequences of noncommuting operators. Trans. Am. Math. Soc. 316, 523–536 (1989)
Popescu, G.: Noncommutative Wold decompositions for semigroups of isometries. Indiana Univ. Math. J. 47, 277–296 (1998)
Popovici, D.: A Wold-type decomposition for commuting isometric pairs. Proc. Am. Math. Soc. 132(8), 2303–2314 (2004)
Popovici, D.: Wold decomposition and two-time parameter stationary processes, in Mathematical Theory of Networks and Systems. In: Proceedings of CD of the MTNS-04 Symposium. Leuven (2004)
Rudin, W.: Functional Analysis. McGraw-Hill, New York (1973)
Sarkar, J.: Wold decomposition for doubly commuting isometries. Linear Algebra Appl. 445, 289–301 (2014)
Skalski, A., Zacharias, J.: Wold decomposition for representations of product systems of \(C^*\)-correspondences. Int. J. Math. 19(4), 455–479 (2008)
Słociński, M.: On the Wold-type decomposition of a pair of commuting isometries. Ann. Pol. Math. 37, 255–262 (1980)
Sriram, R., Francos, J.M., Pearlman, W.A.: Texture coding using a Wold decomposition model. IEEE Trans. Image Process. 5, 1382–1386 (1996)
Stitou, Y., Turcu, F., Najim, M., Radouane, L.: 3-D texture model based on the Wold decomposition. In: Proceedings of European Signal Processing, pp. 429–432. Wien (2004)
Suciu, I.: On the semigroups of isometries. Stud. Math. 30, 101–110 (1968)
Timotin, D.: Regular dilations and models for multicontractions. Indiana Univ. Math. J. 47(2), 671–684 (1998)
Wold, H.: A Study in the Analysis of Stationary Time Series, 2nd edn. Almqvist and Wiksell, Stockholm (1954)
