相关论文: Hyperbolic secants yield Gabor frames
Motivated by the recent work of Bownik and Ross \cite{BR}, and Jakobsen and Lemvig \cite{JL}, this article generalizes latest results on reproducing formulas for generalized translation invariant (GTI) systems to the setting of super-spaces…
The object of study of this article is compact surfaces in the three-dimensional hyperbolic space with a positive-definite second fundamental form. It is shown that several conditions on the Gaussian curvature of the second fundamental form…
Relativistic hadronic plasmas can become under certain conditions supercritical, abruptly and efficiently releasing the energy stored in protons through photon outbursts. Past studies have tried to relate the features of such hadronic…
Suppose G is a Gromov hyperbolic group, and the boundary at infinity of G is quasisymmetrically homeomorphic to an Ahlfors Q-regular metric 2-sphere Z with Ahlfors regular conformal dimension Q. Then G acts discretely, cocompactly, and…
We analyze gauge theories based on abelian $p-$forms in real compact hyperbolic manifolds. The explicit thermodynamic functions associated with skew--symmetric tensor fields are obtained via zeta--function regularization and the trace…
We show that the frame measure function of a frame in certain reproducing kernel Hilbert spaces on metric measure spaces is given by the reciprocal of the Beurling density of its index set. In addition, we show that each such frame with…
We study the kinetic Ising model under Glauber dynamics and establish an upper bound on the spectral gap for finite systems. This bound implies the critical exponent inequality $z \geq 2$, thereby rigorously improving the previously known…
We characterize the entire functions $P$ of $d$ variables, $d\ge 2,$ for which the $\mzd$-translates of $P\chi_{[0,N]^d}$ satisfy the partition of unity for some $N\in \mn.$ In contrast to the one-dimensional case, these entire functions…
Gaussian beams are asymptotically valid high frequency solutions to hyperbolic partial differential equations, concentrated on a single curve through the physical domain. They can also be extended to some dispersive wave equations, such as…
In this paper we construct frames of Gabor type for the space $L^2_{rad}(\R^d)$ of radial $L^2$-functions, and more generally, for subspaces of modulation spaces consisting of radial distributions. Hereby, each frame element itself is a…
We study the thermodynamical properties of a one-dimensional gas with one-dimensional gravitational interactions, and placed in a uniform mass background. Periodic boundary conditions are implemented as a modification of the potential…
Recently precise results for the boundary between the Mott insulator phase and the superfluid phase of the homogeneous Bose-Hubbard model have become available for arbitrary integer filling factor g and any lattice dimension d > 1. We use…
We investigate the holographic $p$-wave superconductors in the presence of the higher order corrections on the gravity as well as on the gauge field side. On the gravity side, we add the Gauss-Bonnet curvature correction terms, while on the…
We report results of large-scale Monte Carlo simulations of superfluid--insulator transitions in commensurate 2D bosonic systems. In the case of off-diagonal disorder (quantum percolation), we find that the transition is to a gapless…
The distinctive features of single field inflationary models with non-minimal kinetic terms, like Dirac-Born-Infeld and k-inflation, can be captured by more familiar multiple field inflationary systems of the type that typically arise in…
In this work we determine the critical exponent for a weakly coupled system of semilinear wave equations with distinct scale-invariant lower order terms, when these terms make both equations in some sense parabolic-like. For the blow-up…
The two-dimensional XY gauge glass, which describes disordered superconducting grains in strong magnetic fields, is investigated, with regard to the possibility of a glass transition. We compute the glass susceptibility and the correlation…
Let $a$, $b$ be two fixed non-zero constants. A measurable set $E\subset \mathbb{R}$ is called a Weyl-Heisenberg frame set for $(a, b)$ if the function $g=\chi_{E}$ generates a Weyl-Heisenberg frame for $L^2(\mathbb{R})$ under modulates by…
Hyperbolic lattices interpolate between finite-dimensional lattices and Bethe lattices and are interesting in their own right with ordinary percolation exhibiting not one, but two, phase transitions. We study four constraint percolation…
We prove that a partially hyperbolic attracting set for a C2 vector field, having slow recurrence to equilibria, supports an ergodic physical/SRB measure if, and only if, the trapping region admits non-uniform sectional expansion on a…