Geodesic
On spectral decompositions of functions in $H_p^\alpha$
Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 1-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is devoted to a study of the spectral resolutions $E_\lambda f$ and their Riesz means $E_\lambda^sf$, corresponding to selfadjoint extensions of elliptic differential operators $A(x,D)$ of order $m$ in an $N$-dimensional domain $G$. It is proved that if $f$ belongs to the Nikol'skii class $\overset\circ H{}_p^\alpha(G)$ and has compact support in $G$, then for $$ \alpha>0,\quad s\geqslant0,\quad\alpha+s\geqslant\frac{N-1}2,\quad p\alpha>N $$ the Riesz means $E_\lambda^sf$ converge for $\lambda\to\infty$ to $f$ uniformly on each compact set $K\subset G$. Bibliography: 9 titles. 
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Sh. A. Alimov. On spectral decompositions of functions in $H_p^\alpha$. Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 1-16. http://geodesic.mathdoc.fr/item/SM_1976_30_1_a0/

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[2] S. M. Nikolskii, Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, izd-vo «Nauka», Moskva, 1969 | MR

[3] Sh. A. Alimov, V. A. Ilin, “O spektralnykh razlozheniyakh, otvechayuschikh proizvolnomu neotritsatelnomu samosopryazhennomu rasshireniyu operatora Laplasa”, DAN SSSR, 193:1 (1970), 9–12 | MR | Zbl

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[5] V. A. Ilin, Sh. A. Alimov, “Usloviya skhodimosti spektralnykh razlozhenii, otvechayuschikh samosopryazhennym rasshireniyam ellipticheskikh operatorov, V”, Diff. uravneniya, 10:3 (1974), 481–506 | MR

[6] Sh. A. Alimov, “Ravnomernaya skhodimost i summiruemost spektralnykh razlozhenii funktsii iz $L_p^\alpha$”, Diff. uravneniya, 9:4 (1973), 669–681 | MR | Zbl

[7] L. Khermander, “O srednikh Rissa spektralnykh funktsii ellipticheskikh differentsialnykh operatorov i sootvetstvuyuschikh spektralnykh razlozheniyakh”, Matematika, 12:5 (1968), 91–130

[8] Sh. A. Alimov, “Drobnye stepeni ellipticheskikh operatorov i izomorfizm klassov differentsiruemykh funktsii”, Diff. uravneniya, 8:9 (1972), 1609–1626 | MR | Zbl

[9] L. Khermander, “Spektralnaya funktsiya ellipticheskogo operatora”, Matematika, 13:6 (1969), 114–137