Localization and convergence of eigenfunction expansions (Q1808998)

The localization principle for expansions in eigenfunctions of a self-adjoint second order elliptic operator is stated. One of the most interesting results concerned with the problem of localization of multiple Fourier integrals is contained in Theorem 1 and in Corollary 3. The last result associated with piecewise smooth functions of two variables is developed in Section 4. Another interesting result contained in Theorem 3 is concerned with the Gibbs phenomenon. It was added in proof, that the authors have obtained some results on convergence of Bochner-Riesz means. The list of references contains 25 items, but it would be useful to add two more articles. One of them is the little known (perhaps it was published in Russian) article by \textit{V. A. Il'in} [Dokl. Akad. Nauk SSSR 109, 442-445 (1956; Zbl 0073.08104)]. The other one is the article by \textit{B. I. Golubov} [Anal. Math. 4, 269-287 (1978; Zbl 0422.42012)].