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Babenko K.I. On conjugated functions, DAN SSSR, vol.62, No2, 1948, pp.157-160.

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Article

Frames from Cosines with the Degenerate Coefficients

1Institute of Mathematics and Mechanics of NAS of Azerbaijan, B.Vahabzade 9, AZ1141,Baku, Azerbaijan


American Journal of Applied Mathematics and Statistics. 2013, Vol. 1 No. 3, 36-40
DOI: 10.12691/ajams-1-3-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Sadigova Sabina Rahib, Mamedova Zahira Vahid. Frames from Cosines with the Degenerate Coefficients. American Journal of Applied Mathematics and Statistics. 2013; 1(3):36-40. doi: 10.12691/ajams-1-3-1.

Correspondence to: Sadigova Sabina Rahib, Institute of Mathematics and Mechanics of NAS of Azerbaijan, B.Vahabzade 9, AZ1141,Baku, Azerbaijan. Email: s_sadigova@mail.ru

Abstract

The system of cosines with a degenerate coefficient in exponential form is considered. A necessary and sufficient condition on the degree of degeneration is found that makes the considered system a frame in Lebesgue spaces. It is proved that if the degenerate coefficient satisfies the Muckenhoupt condition, then the basicity holds. If the Muckenhoupt condition does not hold, then the system has a finite defect, and does not form a frame.

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