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Journal of Function Spaces
Volume 2017 (2017), Article ID 9257076, 4 pages
https://doi.org/10.1155/2017/9257076
Letter to the Editor

Comment on “On the Frame Properties of Degenerate System of Sines”

Institute of Mathematics and Mechanics NAS of Azerbaijan, B. Vahabzade 9, 1141 Baku, Azerbaijan

Correspondence should be addressed to Aydin Sh. Shukurov

Received 26 May 2016; Accepted 8 December 2016; Published 15 March 2017

Academic Editor: Yoshihiro Sawano

Copyright © 2017 Aydin Sh. Shukurov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Bilalov and F. Guliyeva, “On the frame properties of degenerate system of sines,” Journal of Function Spaces and Applications, vol. 2012, Article ID 184186, 12 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  2. K. I. Babenko, “On conjugate functions,” Doklady Akademii Nauk SSSR, vol. 62, pp. 157–160, 1948 (Russian). View at Google Scholar · View at MathSciNet
  3. B. T. Bilalov and Z. A. Gasimov, “On completeness of exponent system with complex coefficients in weight spaces,” Transactions of National Academy of Sciences of Azerbaijan, vol. 25, no. 7, pp. 9–14, 2005. View at Google Scholar · View at MathSciNet
  4. B. T. Bilalov and S. G. Veliev, “Bases of eigenfunctions of two discontinuous differential operators,” Differential Equations, vol. 42, no. 10, pp. 1503–1506, 2006. View at Publisher · View at Google Scholar
  5. K. S. Kazaryan and P. I. Lizorkin, “Multipliers, bases and unconditional bases of the weighted spaces B and SB,” Trudy Matematicheskogo Instituta imeni VA Steklova, vol. 187, pp. 98–115, 1989. View at Google Scholar
  6. S. S. Pukhov and A. M. Sedletski, “Bases of exponentials, sines, and cosines in weighted spaces on a finite interval,” Doklady Akademii Nauk, vol. 425, no. 4, pp. 452–455, 2009. View at Google Scholar
  7. E. I. Moiseev, “On the basis property of sine and cosine systems in a weighted space,” Differentsial'nye Uravneniya, vol. 34, no. 1, pp. 40–44, 1998. View at Google Scholar
  8. E. I. Moiseev, “The basis property of a system of eigenfunctions of a differential operator in a weighted space,” Differentsial'nye Uravneniya, vol. 35, no. 2, pp. 200–205, 1999. View at Google Scholar · View at MathSciNet
  9. E. S. Golubeva, “The system of weighted exponentials with power weights, completeness of sine systems with degenerate coefficients 7 Vestnik Sam. GU,” Estestvenno-Nauchnaya Seriya, vol. 2, no. 83, pp. 15–25, 2011 (Russian). View at Google Scholar
  10. Z. V. Mamedova, “On basis properties of degenerate exponential system,” Applied Mathematics, vol. 3, pp. 1963–1966, 2012. View at Publisher · View at Google Scholar
  11. S. R. Sadigova and Z. V. Mamedova, “Frames from cosines with the degenerate coefficients,” American Journal of Applied Mathematics and Statistics, vol. 1, no. 3, pp. 36–40, 2013. View at Google Scholar
  12. B. T. Bilalov and Z. V. Mamedova, “On the frame properties of some degenerate trigonometric systems,” Doklady. Natsionalnaya Akademiya Nauk Azerbaidzhana, vol. 68, no. 5, pp. 14–18, 2012. View at Google Scholar · View at MathSciNet
  13. B. T. Bilalov and F. A. Gulieva, “A completeness criterion for a double power system with degenerate coefficients,” Siberian Mathematical Journal, vol. 54, no. 3, pp. 536–543, 2013. View at Google Scholar · View at MathSciNet
  14. V. F. Gaposhkin, “A generalization of the theorem of M. Riesz on conjugate functions,” Matematicheskii Sbornik, vol. 46, no. 88, pp. 359–372, 1958. View at Google Scholar · View at MathSciNet
  15. B. T. Bilalov and S. R. Sadigova, “Frame properties of a part of an exponential system with degenerate coefficients in Hardy classes,” Georgian Mathematical Journal, 2016. View at Publisher · View at Google Scholar
  16. N. K. Bari, “Biorthogonal systems and bases in Hilbert space,” Uchenie zapiski Moskovskoqo Gosudarstvennoqo Universiteta, vol. 148, no. 4, pp. 69–107, 1951 (Russian). View at Google Scholar
  17. C. Heil, A Basis Theory Primer, Birkhauser, 2011.