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Summability of eigenfunction expansions of differential operators and convolution operators

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Literature Cited

  1. A. A. Shkalikov, "Completeness of eigen and associated functions of an ordinary differential operator with nonregular uncoupled boundary conditions," Funkts. Anal. Prilozhen.,10, No. 4, 69–80 (1976).

    Google Scholar 

  2. A. P. Khromov, "Finite-dimensional perturbations of Volterra operators," Doctoral Dissertation, Novosibirsk (1973).

  3. A. P. Khromov, "Expansions in eigenfunctions of ordinary linear differential operators with nonregular uncoupled boundary conditions," Mat. Sb.,70, 310–329 (1966).

    Google Scholar 

  4. M. A. Naimark, Linear Differential Operators, Ungar.

  5. A. P. Khromov, "On summability of expansion in the eigenfunctions of a boundary problem for an ordinary differential equation with uncoupled boundary conditions and an analog of a theorem of Weierstrass," in: Ordinary Differential Equations and Fourier Series Expansions [in Russian], Saratovsk Univ. (1968).

  6. B. V. Lidskii, "On summability on series in the principal vectors of non-self-adjoint operators," Tr. Mosk. Mat. Ob-va,11, 3–35 (1962).

    Google Scholar 

  7. B. V. Pal'tsev, "Asymptotic behavior of the eigenvalues of integral convolution operators on a finite interval with kernels having rational Fourier transform," Dokl. Akad. Nauk SSSR,194, No. 4, 774–777 (1970).

    Google Scholar 

  8. B. V. Pal'tsev, "Expansions in the eigenfunctions of integral convolution operators on a finite interval with kernels having rational Fourier transform," Izv. Akad. Nauk SSSR, Ser. Mat.,36, 591–634 (1972).

    Google Scholar 

  9. Yu. I. Lyubarskii, "On the convolution operator on a finite interval," Usp. Mat. Nauk,31, No. 3, 221 (1976).

    Google Scholar 

  10. A. Zygmund, Trigonometric Series, Cambridge Univ. Press (1968).

  11. B. Ya. Levin, Distribution of Zeros of Entire Functions, Amer. Math. Soc. (1964).

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Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 12, No. 4, pp. 24–40, October–December, 1978.

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Kostyuchenko, A.G., Shkalinov, A.A. Summability of eigenfunction expansions of differential operators and convolution operators. Funct Anal Its Appl 12, 262–276 (1978). https://doi.org/10.1007/BF01076380

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  • DOI: https://doi.org/10.1007/BF01076380

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