Piecewise-polynomial approximation of functions fromHℓ((0, 1)d), 2ℓ=d, and applications to the spectral theory of the Schrödinger operator
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- Solomyak, M. Israel J. Math. (1994) 86: 253. doi:10.1007/BF02773681
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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 weightedL2-approximation of functions from the Sobolev spaces in the cases corresponding to the critical exponent in the embedding theorem.