This article is cited in 13 papers

A resonance theorem and series in eigenfunctions of the Laplacian

E. M. Nikishin


Abstract: By means of a resonance theorem we will establish the existence of functions in $L_p(\Omega)$ (where $\Omega$ is an $N$-dimensional region) whose expansion in eigenfunctions of the Laplacian is not Riesz-summable of order $a<N\bigl(\frac1p-\frac12\bigr)-\frac12$ if $1\leqslant p<\frac{2N}{N+1}$.

UDC: 517.5

MSC: Primary 35P10, 40G99; Secondary 42A60

Received: 07.12.1970

 English version: Mathematics of the USSR-Izvestiya, 1972, 6:4, 788–806

Bibliographic databases:

• 
•