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Abstrakty
In this paper, we fix N -many l2-Hilbert spaces Hk whose dimensions are [formula] for k=1,…, N, for N ∈N\{1}. And then, construct a Hilbert space ℑ = ℑ [H1 , . . . , HN] induced by H1 , . . . , HN, and study certain types of operators on ℑ. In particular, we are interested in so-called jump-shift operators. The main results (i) characterize the spectral properties of these operators, and (ii) show how such operators affect the semicircular law induced by [formula], where Bk are the orthonormal bases of Hk , for k = 1, . . . , N.
Czasopismo
Rocznik
Tom
Strony
755--803
Opis fizyczny
Bibliogr. 24 poz.
Twórcy
autor
- St. Ambrose University Department of Mathematics and Statistics 518 W. Locust St., Davenport, Iowa, 52803, U.S.A.
Bibliografia
- [1] M. Ahsanullah, Some inferences on semicircular distribution, J. Stat. Theory Appl. 15 (2016), no. 3, 207-213.
- [2] D. Alpay, P. Jorgensen, Spectral theory for Gaussian processes: reproducing kernels, boundaries, and L2 -wavelet generators with fractional scales, Numer. Funct. Anal. Optim. 36 (2015), no. 10, 1239-1285.
- [3] D. Alpay, P. Jorgensen, D. Levanony, On the equivalence of probability spaces, J. Theoret. Probab. 30 (2017), no. 3, 813-841.
- [4] D. Alpay, P. Jorgensen, D. Levanony, A class of Gaussian processes with fractional spectral measures, J. Funct. Anal. 261 (2011), no. 2, 507-541.
- [5] D. Alpay, P. Jorgensen, G. Salomon, On free stochastic processes and their derivatives, Stochastic Process. Appl. 124 (2014), no. 10, 3392-3411.
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- [7] M. Bozheiko, E.V. Litvinov, I.V. Rodionova, An extended anyon Fock space and non-commutative Meixner-type orthogonal polynomials in the infinite-dimensional case, Uspekhi Mat. Nauk 70 (2015), no. 5, 75-120, translation in Russian Math. Surveys 70 (2015), no. 5, 857-899
- [8] M. Bożejko, W. Ejsmont, T. Hasebe, Noncommutative probability of type D, Internat. J. Math. 28 (2017), no. 2, 1750010, 30 pp.
- [9] I. Cho, Banach *-algebras generated by semicircular elements induced by certain orthog¬onal projections, Opuscula Math. 38 (2018), no. 4, 501-535.
- [10] I. Cho, Semicircular-like laws and the semicircular law induced by orthogonal projections, Complex Anal. Oper. Theory 12 (2018), no. 7, 1657-1695.
- [11] I. Cho, Certain Banach-space operators acting on the semicircular elements induced by orthogonal projections, Mathematical Modelling, Applied Analysis and Computation, 1-39, Springer Proc. Math. Stat., 272, Springer, Singapore, 2019.
- [12] I. Cho, J. Dong, Catalan numbers and free distributions of mutual ly free multisemicircular elements, (2018), submitted.
- [13] I. Cho, P.E.T. Jorgensen, Semicircular Elements Induced by Projections on Separable Hilbert Spaces, Linear Systems, Signal Processing and Hypercomplex Analysis, Oper. Theory Adv. Appl., 275, Linear Oper. Linear Syst., Birkhäuser/Springer, Cham, 2019, 167-209.
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Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-f7061df6-1b3e-4276-bce1-788b0a8d8a82