Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Solomyak, Michael"'
Autor:
Rozenblum, Grigori, Solomyak, Michael
The problem of finding eigenvalue estimates for the Schr\"odinger operator turns out to be most complicated for the dimension 2. Some important results for this case have been obtained recently. We discuss these results and establish their counterpar
Externí odkaz:
http://arxiv.org/abs/1208.6372
Autor:
Solomyak, Michael
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 on the properties of the function $G$ and the value of the coupling par
Externí odkaz:
http://arxiv.org/abs/1203.1156
Autor:
Laptev, Ari, Solomyak, Michael
For a two-dimensional Schr\"odinger operator $H_{\alpha V}=-\Delta-\alpha V$ with the radial potential $V(x)=F(|x|), F(r)\ge 0$, we study the behavior of the number $N_-(H_{\alpha V})$ of its negative eigenvalues, as the coupling parameter $\alpha$ t
Externí odkaz:
http://arxiv.org/abs/1108.1002
Autor:
Rozenblum, Grigori, Solomyak, Michael
The construction of "sparse potentials", suggested in \cite{RS09} for the lattice $\Z^d,\ d>2$, is extended to a wide class of combinatorial and metric graphs whose global dimension is a number $D>2$. For the Schr\"odinger operator $-\D-\a V$ on such
Externí odkaz:
http://arxiv.org/abs/1104.3455
Autor:
Rozenblum, Grigori, Solomyak, Michael
The behavior of the discrete spectrum of the Schr\"odinger operator $-\D - V$, in quite a general setting, up to a large extent is determined by the behavior of the corresponding heat kernel $P(t;x,y)$ as $t\to 0$ and $t\to\infty$. If this behavior i
Externí odkaz:
http://arxiv.org/abs/1005.2690
Autor:
Rozenblum, Grigori, Solomyak, Michael
For the discrete Schr\"odinger operator we obtain sharp estimates for the number of negative eigenvalues.
Externí odkaz:
http://arxiv.org/abs/0905.0270
Autor:
Solomyak, Michael
We discuss estimates on the number $N_-(\alpha)$ of negative eigenvalues of the Schr\"odinger operator $-\Delta-\alpha V$ on regular metric trees, as depending on the properties of the potential $V\ge 0$ and on the value of the large parameter $\alph
Externí odkaz:
http://arxiv.org/abs/0809.0752
Autor:
Friedlander, Leonid, Solomyak, Michael
We consider the Dirichlet Laplacian in a family of narrow unbounded domains. As the width of these domains goes to 0, we study the asymptotic behavior of the eigenvalues that lie below the essential spectrum and the asymptotic behavior of the corresp
Externí odkaz:
http://arxiv.org/abs/0710.1886
Autor:
Friedlander, Leonid, Solomyak, Michael
We derive a two-terms asymptotics for eigenvalues of the Dirichlet Laplacian in a narrow strip of variable width. The asymptotics is taken with respect to a small paprameter that characterizes the width of the strip.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/0705.4058
Autor:
Naboko, Sergey N., Solomyak, Michael
A family $A_\alpha$ of differential operators depending on a real parameter $\alpha\ge 0$ is considered. This family was suggested by Smilansky as a model of an irreversible quantum system. We find the absolutely continuous spectrum $\sigma_{a.c.}$ o
Externí odkaz:
http://arxiv.org/abs/math/0504190