Abstract
In this work an asymptotic formula is obtained for the means of the Riesz spectral function of a homogeneous elliptic operator of arbitrary order m≥2 with constant coefficients. Conditions are obtained under which localization (and convergence) of the means of the Riesz spectral decompositions of functions from the Hölder class is absent.
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V. A. Il'in and Sh. A. Alimov, “Conditions of convergence of spectral decompositions. II, The self-adjoint extension of the Laplace operator with an arbitrary spectrum,” Diff. Urav.,7, No. 5, 851–882 (1971).
V. A. Il'in, “Conditions of convergence of spectral decompositions. IV, Theorems of negative type for an arbitrary extension of a general self-adjoint elliptic second-order differential operator,” Diff. Urav.,9, No. 1, 49–72 (1973).
N. Makhmedzhanov, “On the divergence of kernels of fractional order of spectral decompositions,” Diff, Urav.,9, No. 6, 1141–1142 (1973).
M. V. Fedoryuk, “The method of stationary phases and pseudodifferential operators,” Usp. Matem. Nauk,26, No. 1, 67–112 (1971).
N. N. Lebedev, Special Functions and Their Applications [in Russian], Fizmatgiz, Moscow-Leningrad (1963).
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Translated from Matematicheskie Zametki, Vol. 18, No. 6, pp. 887–894, December, 1975.
In conclusion the author thanks Sh. A. Alimov for constant attention to this work.
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Pulatov, A.K. The divergence of spectral decompositions connected with homogeneous elliptic operators. Mathematical Notes of the Academy of Sciences of the USSR 18, 1115–1118 (1975). https://doi.org/10.1007/BF01099992
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DOI: https://doi.org/10.1007/BF01099992