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Schrodinger operators with potentials generated by primitive substitutions are simple models for one dimensional quasi-crystals. We review recent results on their spectral properties. These include in particular an algorithmically verifiable sufficient condition for their spectrum to be singular continuous and supported on a Cantor set of zero Lebesgue measure. Applications to specific examples are discussed.
Let $mathcal{L}=-Delta+V$ be a Schr{o}dinger operator, where the nonnegative potential $V$ belongs to the reverse H{o}lder class $B_{q}$. By the aid of the subordinative formula, we estimate the regularities of the fractional heat semigroup, ${e^{-tm
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schrodinger operators. It provides more details and suitable extensions to already existing results, that are needed in other recent contributions dealing with these kinds of operators.
We consider a family ${mathcal{H}^varepsilon}_{varepsilon>0}$ of $varepsilonmathbb{Z}^n$-periodic Schrodinger operators with $delta$-interactions supported on a lattice of closed compact surfaces; within a minimal period cell one has $minmathbb{N}$ s
We consider a Schrodinger operator with complex-valued potentials on the line. The operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the positive half-line. We determi
In this work we consider an example of a linear time-degenerate Schrodinger operator. We show that with the appropriate assumptions the operator satisfies a Kato smoothing effect. We also show that the solutions to the nonlinear initial value problem