arXiv subjects

M. Pap

Publications and source records attributed to M. Pap.

3 recordsLinked to original sources

arXiv2018

Unitary equivalence of lowest dimensional reproducing formulae of type $\mathcal{E}_2 \subset Sp(2,{\mathbb R})$

All two-dimensional reproducing formulae, i.e. of $L^2({\mathbb R}^2)$, resulting out of restrictions of the projective metaplectic representation to connected Lie subgroups of $Sp(2,{\mathbb R})$ and of type $\mathcal{E}_2$, were listed and classified up to conjugation within $Sp(2,{\mathbb R})$ in [2], [3]. A full classification, up to conjugation within ${\mathbb R}^2 \rtimes Sp(1,{\mathbb R})$, of one-dimensional reproducing formulae, i.e. of $L^2({\mathbb R})$, resulting out of restrictions of the extended projective metaplectic representation to connected Lie subgroups of ${\mathbb R}^2 \rtimes Sp(1,{\mathbb R})$ was obtained in [13], [14]. In dimension one, there are no reproducing formulae with one-dimensional parametrizations, yet in dimension two, there are reproducing formulae with two-dimensional parametrizations. Two-dimensional reproducing subgroups of $Sp(2,{\mathbb R})$ of type $\mathcal{E}_2$ are a novelty. They exhibit completely new phase space phenomena. We show, that they are all unitarily equivalent via natural choices of coordinate systems, and we derive the consequences of this equivalence.

math.CA↗

arXiv2015

Asymptotic boundary forms for tight Gabor frames and lattice localization domains

We consider Gabor localization operators $G_{\phi,\Omega}$ defined by two parameters, the generating function $\phi$ of a tight Gabor frame $\{\phi_\lambda\}_{\lambda \in \Lambda}$, parametrized by the elements of a given lattice $\Lambda \subset \Bbb{R}^2$, i.e. a discrete cocompact subgroup of $\Bbb{R}^2$, and a lattice localization domain $\Omega \subset \Bbb{R}^2$ with its boundary consisting of line segments connecting points of $\Lambda$. We find an explicit formula for the boundary form $BF(\phi,\Omega)=\text{A}_\Lambda \lim_{R\rightarrow \infty}\frac{PF(G_{\phi,R\Omega})}{R}$, the normalized limit of the projection functional $PF(G_{\phi,\Omega})=\sum_{i=0}^{\infty}\lambda_i(G_{\phi,\Omega})(1-\lambda_i(G_{\phi,\Omega}))$, where $\lambda_i(G_{\phi,\Omega})$ are the eigenvalues of the localization operators $G_{\phi,\Omega}$ applied to dilated domains $R\Omega$, $R$ is an integer and $\text{A}_\Lambda$ is the area of the fundamental domain of the lattice $\Lambda$.

math.CA↗

arXiv2008

Measurements of polarized photo-pion production on longitudinally polarized HD and Implications for Convergence of the GDH Integral

We report new measurements of inclusive pion production from frozen-spin HD for polarized photon beams covering the Delta(1232) resonance. These provide data simultaneously on both H and D with nearly complete angular distributions of the spin-difference cross sections entering the Gerasimov-Drell-Hearn (GDH) sum rule. Recent results from Mainz and Bonn exceed the GDH prediction for the proton by 22 microbarns, suggesting as yet unmeasured high-energy components. Our pi0 data reveal a different angular dependence than assumed in Mainz analyses and integrate to a value that is 18 microbarns lower, suggesting a more rapid convergence. Our results for deuterium are somewhat lower than published data, considerably more precise and generally lower than available calculations.

hep-ex↗