71 citations · 125 across the 18 of their papers we have counts for
18 papers
On spectral estimates for the Schrödinger operators in global dimension 2
Grigori Rozenblum, Michael Solomyak
The problem of finding eigenvalue estimates for the Schrödinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtain…
On a class of spectral problems on the half-line and their applications to multi-dimensional problems
Michael Solomyak
A survey of estimates on the number $N_-(\BM_{\a G})$ of negative eigenvalues (bound states) of the Sturm-Liouville operator $\BM_{\a G}u=-u"-\a G$ on the half-line, as depending o…
On the negative spectrum of two-dimensional Schrödinger operators with radial potentials
Ari Laptev, Michael Solomyak
For a two-dimensional Schrödinger operator with the radial potential , we study the behavior of the number of its negative eige…
Spectral estimates for the Schrödinger operators with sparse potentials on graphs
Grigori Rozenblum, Michael Solomyak
The construction of "sparse potentials", suggested in \cite{RS09} for the lattice , is extended to a wide class of combinatorial and metric graphs whose global dimensio…
On the spectral estimates for Schrödinger type operators. The case of small local dimension
Grigori Rozenblum, Michael Solomyak
The behavior of the discrete spectrum of the Schrödinger operator $-\D - V$, in quite a general setting, up to a large extent is determined by the behavior of the corresponding hea…
On the spectral estimates for the Schrödinger operator on
Grigori Rozenblum, Michael Solomyak
For the discrete Schrödinger operator we obtain sharp estimates for the number of negative eigenvalues.