For citation:
Terekhin P. A. Affine Quantum Frames and Their Spectrum. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 1, pp. 32-36. DOI: 10.18500/1816-9791-2013-13-1-1-32-36, EDN: SMXXHL
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
15.02.2013
Full text:
(downloads: 135)
Language:
Russian
Heading:
UDC:
517.51+517.98
EDN:
SMXXHL
Affine Quantum Frames and Their Spectrum
Autors:
Terekhin Pavel A., Saratov State University
Abstract:
The problem of coefficients quantization for polynomials is solved for affine frames. The problem about coefficients quantization for frame decomposition is considered also. The notion of a spectrum of the quantum frame is introduced. The spectrum of family of affine frames is estimated.
References:
- Casazza P. G., Dilworth S. J., Odell E., Schlumprecht Th., Zsak A. Coefficient quantization for frames in Banach spaces // J. Math. Anal. Appl. 2008. Vol. 348. P. 66–86.
- Терехин П. А. Фреймы в банаховом пространстве // Функц. анализ и его прил. 2010. Т. 44, вып. 3. С. 50–62. [Terekhin P. A. Frames in Banach spaces // Funct. Anal. Appl. 2010. Vol. 44, № 3. P. 199–208.]
- Терехин П. А. Неравенства для компонентов суммируемых функций и их представления по элементам системы сжатий и сдвигов // Изв. вузов. Математика. 1999. № 8. С. 74–81. [Terekhin P. A. Inequalities for the components of summable functions and their representations by elements of a system of contractions and shifts // Russian Math. (Izv. VUZ. Matematika). 1999. Vol. 43, № 8. P. 70—77.]
- Терехин П. А. Аффинные системы функций и фреймы в банаховом пространстве : дис. . . . д-ра физ.-мат. наук. Саратов, 2010. 230 с. [Terekhin P. A. Affine systems of functions and frames in Banach space : Dissertation. Saratov, 2010. 230 p.]
Received:
19.08.2012
Accepted:
22.12.2012
Published:
15.02.2013
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