Jh-Singularity and Jh-Regularity of Multivariate Stationary Processes Over LCA Groups

• Autorzy: Klotz Lutz , Medina Juan Miguel

Identyfikatory

DOI

10.37190/0208-4147.41.1.11

• Języki publikacji: EN

Abstrakty

EN

Let G be an LCA group, Γ its dual group, and H a closed subgroup of G such that its annihilator Λ is countable. Let M denote a regular positive semidefinite matrix-valued Borel measure on Γ and L²(M) the corresponding Hilbert space of matrix-valued functions square-integrable with respect to M. For g∈G, let Z_g be the closure in L²(M) of all matrix-valued trigonometric polynomials with frequencies from g+H. We describe those measures M for which Z_g = L²(M) as well as those for which ∩_g∈GZ_g={0} Interpreting M as a spectral measure of a multivariate wide sense stationary process on G and denoting by J_H the family of H-cosets, we obtain conditions for J_H-singularity and J_H-regularity.

Słowa kluczowe

EN

LCA group; multivariate stationary process; positive semidefinite matrix-valued measure; trigonometric approximation; JH-singularity; JH-regularity; sampling

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2021
• Tom: Vol. 41, Fasc. 1
• Strony: 173--192
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Klotz Lutz

• Fakultät für Mathematik und Informatik, Universität Leipzig, D-04109 Leipzig, Germany

autor

Medina Juan Miguel

• Departamento de Matemática, Facultad de Ingeniería, Universidad de Buenos Aires
• Instituto Argentino de Matemática “A. Calderón”, CONICET Saavedra 15, 3 piso, CABA C1083ACA, Argentina

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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).