Displaying similar documents to “Invariance of essential spectra for generalized Schrödinger operators.”

The L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures

Przemysław Liszka (2014)

Open Mathematics

Similarity:

Very recently bounds for the L q spectra of inhomogeneous self-similar measures satisfying the Inhomogeneous Open Set Condition (IOSC), being the appropriate version of the standard Open Set Condition (OSC), were obtained. However, if the IOSC is not satisfied, then almost nothing is known for such measures. In the paper we study the L q spectra and Rényi dimension of generalized inhomogeneous self-similar measures, for which we allow an infinite number of contracting similarities and...

Optimal measures for the fundamental gap of Schrödinger operators

Nicolas Varchon (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study the potential which minimizes the fundamental gap of the Schrödinger operator under the total mass constraint. We consider the relaxed potential and prove a regularity result for the optimal one, we also give a description of it. A consequence of this result is the existence of an optimal potential under constraints.