A. B. Antonevich, “Coherent Local Hyperbolicity of a Linear Extension and the Essential Spectra of a Weighted Shift Operator on a Closed Interval”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 11–26; Funct. Anal. Appl., 39:1 (2005), 9

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Funktsional'nyi Analiz i ego Prilozheniya, 2005, Volume 39, Issue 1, Pages 11–26
DOI: https://doi.org/10.4213/faa28 (Mi faa28)

This article is cited in 12 scientific papers (total in 12 papers)

Coherent Local Hyperbolicity of a Linear Extension and the Essential Spectra of a Weighted Shift Operator on a Closed Interval

A. B. Antonevich^ab

^a Belarusian State University
^b University of Bialystok

Full-text PDF (225 kB) Citations (12)

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DOI: https://doi.org/10.4213/faa28

Abstract: In the spaces

L_{p}

$L_p$ of vector functions on a closed interval, weighted shift operators

B

$B$ generated by diffeomorphisms of the interval are considered. The notion of coherent local hyperbolicity of the associated linear extension is introduced, and it is established that the closedness of the range of the operator

I - B

$I-B$ is equivalent to coherent local hyperbolicity. On the basis of this result, the description of some essential spectra of the operator

B

$B$ is given.

Keywords: weighted shift operator, essential spectrum, coherent local hyperbolicity.

Received: 03.05.2003

English version:
Functional Analysis and Its Applications, 2005, Volume 39, Issue 1, Pages 9–20
DOI: https://doi.org/10.1007/s10688-005-0013-9

Bibliographic databases:

Document Type: Article

UDC: 517.9

Language: Russian

Citation: A. B. Antonevich, “Coherent Local Hyperbolicity of a Linear Extension and the Essential Spectra of a Weighted Shift Operator on a Closed Interval”, Funktsional. Anal. i Prilozhen., 39:1 (2005), 11–26; Funct. Anal. Appl., 39:1 (2005), 9–20

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/faa28

https://www.mathnet.ru/eng/faa/v39/i1/p11

This publication is cited in the following 12 articles:

A. B. Antonevich, D. I. Kravtsov, “O postanovke kraevykh zadach dlya dvuchlennykh funktsionalnykh uravnenii”, SMFN, 70, no. 3, Rossiiskii universitet druzhby narodov, M., 2024, 343–355
A. B. Antonevich, “Pravostoronnyaya obratimost dvuchlennykh funktsionalnykh operatorov i graduirovannaya dikhotomiya”, Posvyaschaetsya pamyati professora N.D. Kopachevskogo, SMFN, 67, no. 2, Rossiiskii universitet druzhby narodov, M., 2021, 208–236
A. B. Antonevich, A. A. Ahmatova, Ju. Makowska, “Maps with separable dynamics and the spectral properties of the operators generated by them”, Sb. Math., 206:3 (2015), 341–369
Ćemal B. Dolićanin, Anatolij B. Antonevich, Dynamical Systems Generated by Linear Maps, 2014, 185
A. B. Antonevich, E. V. Panteleeva, “Pravostoronnie rezolventy diskretnykh operatorov vzveshennogo sdviga s matrichnymi vesami”, PFMT, 2013, no. 3(16), 45–54
E. V. Panteleeva, “Lokalnye svoistva podmnozhestv, ustoichivykh otnositelno lineinogo rasshireniya”, Tr. In-ta matem., 21:2 (2013), 142–153
Antonevich A.B., Lo S.A., “Polufredgolmovy zadachi o periodicheskikh resheniyakh funktsionalno-differentsialnykh uravnenii neitralnogo tipa”, Differentsialnye uravneniya, 47:10 (2011), 1371–1382
A. B. Antonevich, S. A. Lo, “Semi-Fredholm problems on periodic solutions of functional-differential equations of neutral type”, Diff Equat, 47:10 (2011), 1385
Makowska J., “One-Side Invertibility of the Weighted Shift Operators”, XXIX Workshop on Geometric Methods in Physics, AIP Conference Proceedings, 1307, 2010, 101–105
A. B. Antonevich, Yu. Yakubovska, “Weighted translation operators generated by mappings with saddle points: a model class”, Journal of Mathematical Sciences, 164:4 (2010), 497–517
Antonevich, A, “On Spectral Properties of Weighted Shift Operators Generated by Mappings with Saddle Points”, Complex Analysis and Operator Theory, 2:2 (2008), 215
Makowska J., “On spectral properties of weighted shift operators generated by mappings with saddle points in L-p”, Geometric Methods in Physics, AIP Conference Proceedings, 1079, 2008, 96–101

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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