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Completeness theorem for the dissipative Sturm-Liouville operator on bounded time scales

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  • Hüseyin Tuna

    (Mehmet Akif Ersoy University)

Abstract

In this paper we consider a second-order Sturm-Liouville operator of the form $$l(y): = - [p(t)y^\Delta (t)]^\nabla + q(t)y(t)$$ l ( y ) := − [ p ( t ) y Δ ( t ) ] ∇ + q ( t ) y ( t ) on bounded time scales. In this study, we construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-adjoint and other extensions of the dissipative Sturm-Liouville operators in terms of boundary conditions. Using Krein’s theorem, we proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators on bounded time scales.

Suggested Citation

  • Hüseyin Tuna, 2016. "Completeness theorem for the dissipative Sturm-Liouville operator on bounded time scales," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(3), pages 535-544, September.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:3:d:10.1007_s13226-016-0196-1
    DOI: 10.1007/s13226-016-0196-1
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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    4. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
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