We prove a microlocal version of the equidistribution theorem for Wigner distributions associated to cusp forms on ${\mathrm{PSL}}_2\left(\mathbf{Z}\right)\setminus {\mathrm{PSL}}_2\left(\mathbf{R}\right)$. This generalizes a recent result of W. Luo and P. Sarnak who prove equidistribution on ${\mathrm{PSL}}_2\left(\mathbf{Z}\right)\setminus \mathbf{H}$.

The main object of this work is to describe such weight functions w(t) that for all elements $f\in L_{p,\Omega }$ the estimate $\parallel wf{\parallel }_p\ge K\left(\Omega \right)\parallel f{\parallel }_p$ is valid with a constant K(Ω), which does not depend on f and it grows to infinity when the domain Ω shrinks, i.e. deforms into a lower dimensional convex set ${\Omega }_{\infty }$. In one-dimensional case means that $K\left(\sigma \right):=K\left({\Omega }_{\sigma }\right)\to \infty$ as σ → 0. It should be noted that in the framework of the signal transmission problem such estimates describe a signal’s behavior under the influence of detection and amplification. This work...

The author constructs the gauged Skyrme model by introducing the skyrmion bundle as follows: instead of considering maps $U:M\to {\text{SU}}_{N_F}$ he thinks of the meson fields as of global sections in a bundle $B(M,{\text{SU}}_{N_F},G)=P(M,G){\times }_G{\text{SU}}_{N_F}$. For calculations within the skyrmion bundle the author introduces by means of the so-called equivariant cohomology an analogue of the topological charge and the Wess-Zumino term. The final result of this paper is the following Theorem. For the skyrmion bundle with $N_F\le 6$, one has $$H^{*}\left(EG{\times }_G{\text{SU}}_{N_F}\right)\cong H^{*}{\left({\text{SU}}_{N_F}\right)}^G\cong \text{S}\left({\underline{G}}^{*}\right)\otimes H^{*}\left({\text{SU}}_{N_F}\right)\cong H^{*}\left(BG\right)\otimes H^{*}\left({\text{SU}}_{N_F}\right),$$ where $EG(BG,G)$ is the universal bundle...

The original version of the article was published in Central European Journal of Mathematics, 2008, 6(2), 191–203, DOI: 10.2478/s11533-008-0026-8. Unfortunately, the original version of this article contains a mistake, which we correct here.

The Coupled Cluster (CC) method is a widely used and highly successful high precision method for the solution of the stationary electronic Schrödinger equation, with its practical convergence properties being similar to that of a corresponding Galerkin (CI) scheme. This behaviour has for the discrete CC method been analyzed with respect to the discrete Galerkin solution (the “full-CI-limit”) in [Schneider, 2009]. Recently, we globalized the CC formulation to the full continuous space, giving a root...

We give a condition of essential self-adjointness for magnetic Schrödinger operators on non-compact Riemannian manifolds with a given positive smooth measure which is fixed independently of the metric. This condition is related to the classical completeness of a related classical hamiltonian without magnetic field. The main result generalizes the result by I. Oleinik [29,30,31], a shorter and more transparent proof of which was provided by the author in [41]. The main idea, as in [41], consists...