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Riesz bases formed by root functions of a functional-differential equation with a reflection operator

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Abstract

We find conditions under which the system of root functions of the operator

$$ L_y = l[y] = ay'(x) + y'(1 - x) + p_1 (x)y(x) + p_2 (x)y(1 - x),x \in [0,1],U_1 (y) = \int\limits_0^1 {y(t)d\sigma (t) = 0,} $$

is a Riesz basis in L 2[0, 1].

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References

  1. Babbege, Ch., Philosophical Transactions of the Royal Soc. of London, 1816, vol. 11, pp. 179–256.

    Article  Google Scholar 

  2. Bellman, R. and Cooke, K.L., Differential-Difference Equations, New York: Academic, 1963. Translated under the title Differentsial’no-raznostnye uravneniya, Moscow: Mir, 1967.

    MATH  Google Scholar 

  3. Dunkl, Ch., Trans. Amer. Math. Soc., 1989, vol. 311, no. 1, pp. 167–183.

    Article  MATH  MathSciNet  Google Scholar 

  4. Andreev, A.A. and Saushkin, I.N., Vestn. Samar. Gos. Univ. Fiz-Mat. Nauki, 2005, vol. 36, pp. 10–16.

    Google Scholar 

  5. Platonov, S.S., Tr. Petrozavodsk Gos. Univ. Ser. Mat., 2004, vol. 11, pp. 15–34.

    MathSciNet  Google Scholar 

  6. Khromov, A.P., Mat. Zametki, 1998, vol. 64, no. 6, pp. 932–942.

    MathSciNet  Google Scholar 

  7. Kornev, V.V. and Khromov, A.P., Mat. Sb., 2001, vol. 192, no. 10, pp. 33–50.

    MathSciNet  Google Scholar 

  8. Khromov, A.P., in Matematika. Mekhanika: Sb. nauch. tr. (Mathematics. Mechanics: Collection of Scientific Papers), Saratov: Saratov. Gos. Univ., 2005, issue 7, pp. 130–133.

    Google Scholar 

  9. Shkalikov, A.A., Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1982, no. 6, pp. 12–21.

  10. Shkalikov, A.A., Tr. Semin. im. I.G. Petrovskogo, 1983, vol. 9, pp. 190–229.

    MATH  MathSciNet  Google Scholar 

  11. Baskakov, A.G. and Katsaran, T.K., Differ. Uravn., 1988, vol. 24, no. 8, pp. 1424–1433.

    MathSciNet  Google Scholar 

  12. Rapoport, I.M., O nekotorykh asimptoticheskikh metodakh v teorii differentsial’nykh uravnenii (On Some Asymptotic Methods in the Theory of Differential Equations), Kiev: Izdat. Akad. Nauk Ukrain. SSR, 1954.

    Google Scholar 

  13. Kurdyumov, V.P. and Khromov, A.P., Mat. Zametki, 2004, vol. 76, no. 1, pp. 97–110.

    MathSciNet  Google Scholar 

  14. Sedletskii, A.M., Sovrem. Mat. Fundam. Napravl., 2003, vol. 5, pp. 3–152.

    Google Scholar 

  15. Kurdyumov, V.P. and Khromov, A.P., in Matematika. Mekhanika: Sb. nauch. tr. (Mathematics. Mechanics: Collection of Scientific Papers), Saratov: Saratov. Gos. Univ., 2004, issue 6, pp. 80–82.

    Google Scholar 

  16. Naimark, M.A., Lineinye differentsial’nye operatory (Linear Differential Operators), Moscow: Nauka, 1969.

    Google Scholar 

  17. Kurdyumov, V.P. and Khromov, A.P., in Matematika. Mekhanika: Sb. nauch. tr. (Mathematics. Mechanics: Collection of Scientific Papers), Saratov: Saratov. Gos. Univ., 2005, issue 7, pp. 61–63.

    Google Scholar 

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Authors and Affiliations

  1. Saratov State University, Saratov, Russia

    V. P. Kurdyumov & A. P. Khromov

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  1. V. P. Kurdyumov
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  2. A. P. Khromov
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Original Russian Text © V.P. Kurdyumov, A.P. Khromov, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 2, pp. 196–204.

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Kurdyumov, V.P., Khromov, A.P. Riesz bases formed by root functions of a functional-differential equation with a reflection operator. Diff Equat 44, 203–212 (2008). https://doi.org/10.1134/S0012266108020079

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  • DOI: https://doi.org/10.1134/S0012266108020079

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