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@article{FAA_2022_56_1_a3, author = {T. B{\^\i}nzar and C. L\u{a}zureanu}, title = {Wold-type decompositions for pairs of commutative semigroups generated by isometries}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {51--65}, publisher = {mathdoc}, volume = {56}, number = {1}, year = {2022}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_1_a3/} }
TY - JOUR AU - T. Bînzar AU - C. Lăzureanu TI - Wold-type decompositions for pairs of commutative semigroups generated by isometries JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 2022 SP - 51 EP - 65 VL - 56 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_2022_56_1_a3/ LA - ru ID - FAA_2022_56_1_a3 ER -
T. Bînzar; C. Lăzureanu. Wold-type decompositions for pairs of commutative semigroups generated by isometries. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 1, pp. 51-65. http://geodesic.mathdoc.fr/item/FAA_2022_56_1_a3/
[1] C. A. Berger, L. A. Coburn, A. Lebow, “Representation and index theory for $C^*$-algebras generated by commuting isometries”, J. Funct. Anal., 27 (1978), 51–99 | DOI | MR | Zbl
[2] T. Bînzar, C. Lăzureanu, “On the Wold-type decompositions for $n$-tuples of commuting isometric semigroups”, Filomat, 31:5 (2017), 1251–1264 | DOI | MR
[3] T. Bînzar, Z. Burdak, C. Lăzureanu, D. Popovici, M. Słociński, “Wold–Słociński decompositions for commuting isometric triples”, J. Math. Anal. Appl., 472:2 (2019), 1660–1677 | DOI | MR
[4] Z. Burdak, “On decomposition of pairs of commuting isometries”, Ann. Polon. Math., 84:2 (2004), 121–135 | DOI | MR | Zbl
[5] D. Gaşpar, N. Suciu, “Wold decompositions for commutative families of isometries”, An. Univ. Timişoara Ser. Stiint. Mat., 27 (1989), 31–38 | MR
[6] P. R. Halmos, “Shifts on Hilbert spaces”, J. Reine Angew. Math., 208 (1961), 102–112 | DOI | MR | Zbl
[7] G. Kallianpur, V. Mandrekar, “Nondeterministic random fields and Wold and Halmos decompositions for commuting isometries”, Prediction theory and harmonic analysis, North-Holland, Amsterdam, 1983, 165–190 | MR
[8] F. Liu, R. W. Picard, “A spectral 2-D Wold decomposition algorithm for homogeneous random fields”, Proceedings of the International Conference on Acoustics, Speech and Signal Processing (Phoenix, Arizona, USA, 1999), v. 4, IEEE, Piscataway, 1999, 3501–3504 | MR
[9] J. von Neumann, “Allgemeine eigenwerttheorie hermitischer funktional operatoren”, Math. Ann., 102 (1929), 49–131 | MR | Zbl
[10] F. Pater, L. D. Lemle, T. Bînzar, “On a Wold–Słociński's type decomposition of a pair of commuting semigroups of isometries”, Proceendings of the International Conference of Numerical Analysis and Applied Mathematics (Rhodes, Greece, 2010), Amer. Inst. of Phys., College Park, 2010, 1379–1381
[11] D. Popovici, “A Wold-type decomposition for commuting isometric pairs”, Proc. Amer. Math. Soc., 132:8 (2004), 2303–2314 | DOI | MR | Zbl
[12] U. Rudin, Funktsionalnyi analiz, Mir, M., 1973 | MR
[13] M. Słociński, “On the Wold-type decomposition of a pair of commuting isometries”, Ann. Polon. Math., 37:3 (1980), 255–262 | DOI | MR
[14] Y. Stitou, F. Turcu, M. Najim, L. Radouane, “3-D texture model based on the Wold decomposition”, Proceedings of the 12th European Signal Processing Conference (Vienna, Austria, 2004), IEEE, Piscataway, 2004, 429–432
[15] I. Suciu, “On the semigroups of isometries”, Studia Math., 30 (1968), 101–110 | DOI | MR | Zbl
[16] B. Sz.-Nagy, C. Foiaş, H. Bercovici, L. Kérchy, Harmonic Analysis of Operators on Hilbert Spaces, 2nd, Springer-Verlag, New York, 2010 | MR
[17] H. Wold, A Study in the Analysis of Stationary Time Series, Almqvist and Wiksell, Stockholm, 1954 | MR | Zbl