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Contemporary Mathematics. Fundamental Directions, 2008, Volume 29, Pages 29–48
(Mi cmfd122)
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This article is cited in 7 scientific papers (total in 7 papers)
Weighted translation operators generated by mappings with saddle points: a model class
A. B. Antonevichab, Yu. Yakubovskab a Belarusian State University
b University of Bialystok
Abstract:
A particular class of weighted translation operators $B$ generated by mappings with saddle points are considered. For $\lambda$ belonging to the spectrum of the operator $B$, a description of properties of the operator $B-\lambda I$ is found. In particular, necessary and sufficient conditions of one-side invertibility are found. It follows from the obtained results that weighted translation operators generated by mappings with saddle points have principally different spectral properties compared to weighted translation operators generated by mappings without saddle points (investigated earlier).
It is proved that the operator $B-I$ is one-side invertible if and only if a certain property of a linear extension associated with the operator $B$ holds.
Citation:
A. B. Antonevich, Yu. Yakubovska, “Weighted translation operators generated by mappings with saddle points: a model class”, Proceedings of the Crimean autumn mathematical school-symposium, CMFD, 29, PFUR, M., 2008, 29–48; Journal of Mathematical Sciences, 164:4 (2010), 497–517
Linking options:
https://www.mathnet.ru/eng/cmfd122 https://www.mathnet.ru/eng/cmfd/v29/p29
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Abstract page: | 444 | Full-text PDF : | 102 | References: | 47 |
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