Bounded divergence of expansions in eigenfunctions of the Laplace operator (Q1078762)

Conditions of localisation of the expansion of the spectral resolution \(E_{\lambda} f(x)\) into the Fourier series in eigenfunctions of the Laplace operator are studied, the functions f being assumed to belong to the Nikolskij space \(H_ p^{\alpha}\). In the main theorem the existence of a function \(f\in H_ p^{\alpha}\) is proved which yields bounded divergence of \(E_{\lambda} f\), i.e. \(\lim_{\lambda \to \infty}| E_{\lambda} f(x)| >0\), in a more general case than the author proved in his previous paper.