Spectral synthesis in weighted Sobolev spaces (Q1363829)

The author generalizes Hedberg's results on spectral synthesis in Sobolev spaces to the case of weighted Sobolev spaces whose weights satisfy the Muckenhoupt condition. The density of the set of compactly supported smooth functions is proved using techniques of weighted nonlinear potential theory and embeddings theorems. The \(L_q\) approximation by solutions of elliptic equations is also considered and necessary and sufficient conditions are given for the stability in weighted Sobolev spaces. The results have been announced in [Math. Notes 56, No. 2, 856-858 (1994); translation from Mat. Zametki 56, No. 2, 136-139 (1994; Zbl 0851.46025)].