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 Differ. Uravn., 1971, Volume 7, Number 4, Pages 670–710 (Mi de1255)

Partial Differential Equations

Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. I. Self-adjoint extension of the Laplace operator with a point spectrum

V. A. Il'in, Sh. A. Alimov

Lomonosov Moscow State University

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Bibliographic databases:
UDC: 517.518.45.517.95

Citation: V. A. Il'in, Sh. A. Alimov, “Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. I. Self-adjoint extension of the Laplace operator with a point spectrum”, Differ. Uravn., 7:4 (1971), 670–710

Citation in format AMSBIB
\Bibitem{IliAli71} \by V.~A.~Il'in, Sh.~A.~Alimov \paper Conditions for the convergence of spectral decompositions that correspond to self-adjoint extensions of elliptic operators. I. Self-adjoint extension of the Laplace operator with a point spectrum \jour Differ. Uravn. \yr 1971 \vol 7 \issue 4 \pages 670--710 \mathnet{http://mi.mathnet.ru/de1255} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=284867} \zmath{https://zbmath.org/?q=an:0224.35014} 

• http://mi.mathnet.ru/eng/de1255
• http://mi.mathnet.ru/eng/de/v7/i4/p670

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This publication is cited in the following articles:
1. B. I. Golubov, “On the convergence of Riesz spherical means of multiple Fourier series and integrals of functions of bounded generalized variation”, Math. USSR-Sb., 18:4 (1972), 635–658
2. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127
3. Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral decompositions. I”, Russian Math. Surveys, 31:6 (1976), 29–86
4. V. V. Tikhomirov, “On the Riesz means of expansion in eigenfunctions and associated functions of a nonselfadjoint ordinary differntial operator”, Math. USSR-Sb., 31:1 (1977), 29–48
5. Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Problems of convergence of multiple trigonometric series and spectral decompositions. II”, Russian Math. Surveys, 32:1 (1977), 115–139
6. M. I. Dyachenko, “$u$-convergence of multiple Fourier series”, Izv. Math., 59:2 (1995), 353–366
7. M. I. Dyachenko, “Uniform convergence of double Fourier series for classes of functions with anisotropic smoothness”, Math. Notes, 59:6 (1996), 680–686
8. M. I. Dyachenko, “Spherical partial sums of the double Fourier series of functions of bounded generalized variation”, Sb. Math., 188:1 (1997), 29–60
9. M. I. Dyachenko, “Two-dimensional Waterman classes and $u$-convergence of Fourier series”, Sb. Math., 190:7 (1999), 955–972
10. T. G. Ayele, M. L. Goldman, “Spaces of generalised smoothness in summability problems for $\Phi$-means of spectral decomposition”, Eurasian Math. J., 5:1 (2014), 61–81
11. A. A. Rakhimov, “On the uniform convergence of Fourier series on a closed domain”, Eurasian Math. J., 8:3 (2017), 60–69
12. E. Liflyand, “Babenko's work on spherical Lebesgue constants”, Eurasian Math. J., 9:4 (2018), 79–81