Takuya Mine
The Aharonov-Bohm solenoids in a constant magnetic field
(778K, Postscript)

ABSTRACT.  We study the spectral properties of two-dimensional magnetic Schr\"odinger 
operator $H_N= (\frac{1}{i}\nabla + \a_N)^2$. 
The magnetic field is given by 
$\rot \a_N = B+\sum_{j=1}^N 2\pi\alpha_j \delta(z-z_j)$, 
where $B>0$ is a constant, $1\leq N \leq \infty$, 
$0<\alpha_j<1$ $(j=1,\ldots,N)$ 
and the points $\{z_j\}_{j=1}^N$ are uniformly separated. 
We give an upper bound for the number of eigenvalues of $H_N$ 
between two Landau levels or below the lowest Landau level, 
when $N$ is finite. 
We prove the spectral localization of $H_N$ near the spectrum of 
the single solenoid operator, 
when $\{z_j\}_{j=1}^N$ are far from each other, 
all the values $\{\alpha_j\}_{j=1}^N$ are the same and 
the boundary conditions at all $z_j$ are the same. 
We give a characterization of self-adjoint extensions of 
the minimal operator.