17 citations · 19 across the 7 of their papers we have counts for
8 papers
Spectral Properties of Schrödinger Operators with Decaying Potentials
Sergey A. Denisov, Alexander Kiselev
We review recent advances in the spectral theory of Schrödinger operators with decaying potentials. The area has seen spectacular progress in the past few years, stimulated by seve…
On the preservation of absolutely continuous spectrum for Schrodinger operators
Sergey A. Denisov
We present general principles for the preservation of a.c. spectrum under weak perturbations. The Schrodinger operators on the strip and on the Caley tree (Bethe lattice) are consi…
Absolutely continuous spectrum of multidimensional Schrodinger operator
S. A. Denisov
We prove that 3-dimensional Schrodinger operator with slowly decaying potential has an absolutely continuous spectrum that fills the positive half-line. The asymptotics of Green's…
Asymptotics of the orthogonal polynomials for the Szego class with a polynomial weight
S. Denisov, S. Kupin
Let p(t) be a trigonometric polynomial, non-negative on the unit circle. We say that a measure σbelongs to a polynomial Szego class, if the logarithm of its density is summable ove…
The Szego class with a polynomial weight
S. Denisov, S. Kupin
Let p be a trigonometric polynomial, nonnegative on the unit circle . We say that a measure on belongs to the polynomial Szego class, if $dσ=sigma'_{ac…
On the absolutely continuous spectrum of Dirac operator
S. A. Denisov
We prove that the massless Dirac operator in with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued p…