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A completeness criterion for a double power system with degenerate coefficients

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Abstract

We consider a double power system with degenerate coefficients. Under certain conditions we obtain a completeness criterion for this system in the Lebesgue function space.

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References

  1. Walsh J. L., Interpolation and Approximation by Rational Functions in the Complex Domain, Amer. Math. Soc., Providence, R.I. (1965).

    MATH  Google Scholar 

  2. Shkalikov A. A., “A system of functions,” Math. Notes, 18, No. 6, 1097–1100 (1975).

    Article  Google Scholar 

  3. Kaz’min Yu. A., “Closure of the linear span of a system of functions,” Siberian Math. J., 18, No. 4, 565–570 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  4. Kaz’min Yu. A., “Closure of linear spans of two systems of functions,” Dokl. Akad. Nauk SSSR, 236, No. 3, 535–537 (1977).

    MathSciNet  Google Scholar 

  5. Tumarkin A. G., “Completeness of certain systems of functions,” Funct. Anal. Appl., 14, No. 2, 150–151 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  6. Tumarkin A. G., “Completeness and minimality of certain systems of functions,” Siberian Math. J., 24, No. 1, 130–136 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  7. Lyubarskiĭ Yu. I., “The completeness and minimality of the function systems of the form {a(t)ψn(t) − b(t)φ n (t)} ∞ N ,” in: Function Theory, Functional Analysis, and Some of Their Applications [in Russian], Khar-kov, 1988, No. 49, pp. 77–86.

    Google Scholar 

  8. Lyubarskiĭ Yu. I., “Properties of systems of linear combinations of powers,” Leningrad Math. J., 1, No. 6, 1297–1369 (1990).

    MathSciNet  Google Scholar 

  9. Bilalov B. T., “A necessary and sufficient condition for the completeness and minimality of a system of the form \(\{ A(t)\phi ^n (t);B(t)\bar \phi ^n (t)\} \),” Soviet Math., Dokl., 45, No. 1, 211–214 (1992).

    MathSciNet  Google Scholar 

  10. Bilalov B. T., “The basis properties of some systems of exponential functions, cosines, and sines,” Siberian Math. J., 45, No. 2, 214–221 (2004).

    Article  MathSciNet  Google Scholar 

  11. Bilalov B. T., “The basis properties of power systems in Lp,” Siberian Math. J., 47, No. 1, 18–27 (2006).

    Article  MathSciNet  Google Scholar 

  12. Bilalov B. T. and Guseynov Z. G., “Basis properties of unitary systems of powers,” Proc. of Inst. Math. Mech. Natl. Acad. Sci. Azerb., 30, 37–50 (2009).

    MathSciNet  MATH  Google Scholar 

  13. Bilalov B. T., “A system of exponential functions with shift and the Kostyuchenko problem,” Siberian Math. J., 50, No. 2, 223–230 (2009).

    Article  MathSciNet  Google Scholar 

  14. Veliev S. G., “Bases from subsets of eigenfunctions of two discontinuous differential operators,” Mat. Fiz. Anal. Geom., 12, No. 2, 148–157 (2005).

    MathSciNet  MATH  Google Scholar 

  15. Veliev S. G., “Criteria for the completeness and minimality of a system of exponents with singularities,” Bull. Georgian Acad. Sci., 171, No. 1, 21–23 (2005).

    MathSciNet  Google Scholar 

  16. Veliev S. G., “On completeness of eigenfunctions of two discontinuous differential operators,” Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb., 18, 141–146 (2003).

    MathSciNet  MATH  Google Scholar 

  17. Simonenko I. B., “Riemann’s boundary value problem with a continuous coefficient,” Dokl. Akad. Nauk SSSR, 124, No. 2, 278–281 (1959).

    MathSciNet  MATH  Google Scholar 

  18. Simonenko I. B., “Riemann’s boundary problem with a measurable coefficient,” Soviet Math., Dokl., 1, 1295–1298 (1960).

    MathSciNet  MATH  Google Scholar 

  19. Danilyuk I. I., “The Hilbert problem with measurable coefficients,” Sibirsk. Mat. Zh., 1, No. 2, 171–197 (1960).

    MATH  Google Scholar 

  20. Mandzhavidze G. F. and Khvedelidze B. V., “On Riemann-Privalov’s problem with continuous coefficients,” Dokl. Akad. Nauk SSSR, 123, No. 5, 791–794 (1958).

    MathSciNet  MATH  Google Scholar 

  21. Danilyuk I. I., Irregular Boundary Value Problems on the Plane [in Russian], Nauka, Moscow (1975).

    Google Scholar 

  22. Bilalov B. T. and Eminov M. S., “On completeness of a system of powers,” Trans. Mech. Natl. Acad. Sci. Azerb., 26, No. 1, 45–50 (2006).

    MathSciNet  MATH  Google Scholar 

  23. Vekua I. N., Generalized Analytic Functions, Pergamon Press, Oxford, London, New York, and Paris (1962).

    MATH  Google Scholar 

  24. Privalov I. I., Boundary Properties of Analytic Functions [in Russian], GITTL, Moscow (1950).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Baku, Azerbaijan

    B. T. Bilalov & F. A. Guliyeva

Authors
  1. B. T. Bilalov
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  2. F. A. Guliyeva
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Correspondence to B. T. Bilalov.

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Original Russian Text Copyright © 2013 Bilalov B.T. and Guliyeva F.A.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 3, pp. 536–543, May–June, 2013.

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Bilalov, B.T., Guliyeva, F.A. A completeness criterion for a double power system with degenerate coefficients. Sib Math J 54, 419–424 (2013). https://doi.org/10.1134/S0037446613030051

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  • DOI: https://doi.org/10.1134/S0037446613030051

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