P. A. Terekhin, “Multishifts in Hilbert Spaces”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 69–81; Funct. Anal. Appl., 39:1 (2005), 57

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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 1, Pages 69–81
DOI: https://doi.org/10.4213/faa32 (Mi faa32)

This article is cited in 14 scientific papers (total in 14 papers)

Multishifts in Hilbert Spaces

P. A. Terekhin

Saratov State University named after N. G. Chernyshevsky

Full-text PDF (196 kB) Citations (14)

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DOI: https://doi.org/10.4213/faa32

Abstract: We introduce and study a multishift structure in a Hilbert space. This structure is a noncommutative analog of the (simple one-sided) shift operator, well known in function theory and functional analysis. Subspaces invariant under the multishift are described. A theorem on the factorization into an inner and an outer factor is established for operators commuting with the multishift.

Keywords: Hilbert space, shift operator, multishift, invariant subspace, wandering subspace, factorization theorem.

Received: 19.03.2003

English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 1, Pages 57–67
DOI: https://doi.org/10.1007/s10688-005-0017-5

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: P. A. Terekhin, “Multishifts in Hilbert Spaces”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 69–81; Funct. Anal. Appl., 39:1 (2005), 57–67

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa32

https://doi.org/10.4213/faa32

https://www.mathnet.ru/eng/faa/v39/i1/p69

This publication is cited in the following 14 articles:

Astashkin V S., Terekhin P.A.Y., “Sequences of Dilations and Translations Equivalent to the Haar System in l-P-Spaces”, J. Approx. Theory, 274 (2022), 105672
Astashkin S.V., Terekhin P.A., “Sequences of Dilations and Translations in Function Spaces”, J. Math. Anal. Appl., 457:1 (2018), 645–671
S. V. Astashkin, P. A. Terekhin, “Basis properties of affine Walsh systems in symmetric spaces”, Izv. Math., 82:3 (2018), 451–476
S. V. Astashkin, P. A. Terekhin, “Affine Walsh-type systems of functions in symmetric spaces”, Sb. Math., 209:4 (2018), 469–490
Mironov V.A., Sarsenbi A.M., Terekhin P.A., “Affine Bessel Sequences and Nikishin'S Example”, Filomat, 31:4 (2017), 963–966
Astashkin S.V., Terekhin P.A., “On the Boundedness of Operator Generated By the Haar Multishift”, Dokl. Math., 96:2 (2017), 442–444
S.V. Astashkin, P. A. Terekhin, “OB OGRANIChENNOSTI OPERATORA, POROZhDENNOGO MULTISDVIGOM KhAARA, “Doklady Akademii nauk””, Doklady Akademii Nauk, 2017, no. 2, 133
P. A. Terekhin, “Affine Riesz bases and the dual function”, Sb. Math., 207:9 (2016), 1287–1318
Kh. Kh. Kh. Al-Dzhourani, V. A. Mironov, P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Polnota i minimalnost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 247–256
P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Ortogonalizatsiya i popolnenie”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 14:4(1) (2014), 395–400
Sarsenbi A.M., Terekhin P.A., “Riesz Basicity For General Systems of Functions”, J. Funct. space, 2014, 860279
P. A. Terekhin, “Best approximation of functions in $L_p$ by polynomials on affine system”, Sb. Math., 202:2 (2011), 279–306
P. A. Terekhin, “Linear algorithms of affine synthesis in the Lebesgue space $L^1[0,1]$ ”, Izv. Math., 74:5 (2010), 993–1022
P. A. Terekhin, “Convergence of Biorthogonal Series in the System of Contractions and Translations of Functions in the Spaces $L^p[0,1]$ ”, Math. Notes, 83:5 (2008), 657–674

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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