Piecewise-polynomial approximation of functions fromH ℓ((0, 1) d ), 2ℓ=d, and applications to the spectral theory of the Schrödinger operator
- Cite this article as:
- Solomyak, M. Israel J. Math. (1994) 86: 253. doi:10.1007/BF02773681
For the selfadjoint Schrödinger operator −Δ−αV on ℝ2 the number of negative eigenvalues is estimated. The estimates obtained are based upon a new result on the weightedL 2-approximation of functions from the Sobolev spaces in the cases corresponding to the critical exponent in the embedding theorem.