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Nonexistence of localization of spectral decompositions associated with elliptic operators

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Literature cited

  1. V. A. Il'in, “Problems of localization and convergence for Fourier series with respect to fundamental systems of functions of the Laplace operator,” Usp. Mat. Nauk,23, No. 2, 61–120 (1968).

    Google Scholar 

  2. Sh. A. Alimov, “Spectral decompositions of functions from H αp ,” Mat. Sb.,101, No. 1, 3–20 (1976).

    Google Scholar 

  3. A. K. Pulatov, “Localization of spectral decompositions associated with homogeneous elliptic operators,” Dokl. Akad. Nauk SSSR,238, No. 4, 800–803 (1978).

    Google Scholar 

  4. A. K. Pulatov, “Convergence of spectral decompositions associated with homogeneous elliptic operators,” Mat. Zametki,18, No. 6, 887–894 (1975).

    Google Scholar 

  5. G. Bergendal, “Convergence and summability of eigenfunction expansions connected with elliptic differential operators,” Medd. Lunds. Univ. Mat. Sem.,14, 1–63 (1959).

    Google Scholar 

  6. Sh. A. Alimov, “Fractional powers of an elliptic operator,” Diff. Uravn.,8, No. 9, 1602–1626 (1972).

    Google Scholar 

  7. Sh. A. Alimov and V. A. Il'in, “Convergence conditions for spectral decompositions corresponding to self-adjoint extensions of elliptic operators. I,” Diff. Uravn.,7, No. 4, 670–710 (1971).

    Google Scholar 

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Translated from Matematicheskie Zametki, Vol. 30, No. 4, pp. 535–542, October, 1981.

In conclusion, the author thanks Sh. A. Alimov profoundly for directing the work and also thanks A. K. Pulatov for valuable advice.

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Ashurov, R.R. Nonexistence of localization of spectral decompositions associated with elliptic operators. Mathematical Notes of the Academy of Sciences of the USSR 30, 760–764 (1981). https://doi.org/10.1007/BF01137804

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