Geodesic
On spectral decompositions of functions in~$H_p^\alpha$
Sbornik. Mathematics, Tome 30 (1976) no. 1, pp. 1-16

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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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     author = {Sh. A. Alimov},
     title = {On spectral decompositions of functions in~$H_p^\alpha$},
     journal = {Sbornik. Mathematics},
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     url = {http://geodesic.mathdoc.fr/item/SM_1976_30_1_a0/}
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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/