Related papers: Locating resonances on hyperbolic cones
A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of…
We study the distribution of resonances for geometrically finite hyperbolic surfaces of infinite area by countting resonances numerically. The resonances are computed as zeros of the Selberg zeta function, using an algorithm for computation…
We revisit Vasy's method for showing meromorphy of the resolvent for (even) asymptotically hyperbolic manifolds. It provides an effective definition of resonances in that setting by identifying them with poles of inverses of a family of…
The theoretical computing of special values assumed by the hypergeometric functions has a high interest not only on its own, but also in sight of the remarkable implications to both pure Mathematics and Mathematical Physics. Accordingly, in…
For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic…
A method is described to sum multi-dimensional arithmetic functions subject to hyperbolic summation conditions, provided that asymptotic formulae in rectangular boxes are available. In combination with the circle method, the new method is a…
Hyperbolic polynomials are real polynomials whose real hypersurfaces are nested ovaloids, the inner most of which is convex. These polynomials appear in many areas of mathematics, including optimization, combinatorics and differential…
On manifolds with an even Riemannian conformally compact Einstein metric, the resolvent of the Lichnerowicz Laplacian, acting on trace-free, divergence-free, symmetric 2-tensors is shown to have a meromorphic continuation to the complex…
We calculate accurate bound states and resonances of two interesting perturbed Coulomb models by means of the Riccati-Pad\'{e} method. This approach is based on a rational approximation to a modified logarithmic derivative of the…
We present explicit constructions of orthogonal polynomials inside quadratic bodies of revolution, including cones, hyperboloids, and paraboloids. We also construct orthogonal polynomials on the surface of quadratic surfaces of revolution,…
An averaging method for getting uniformly valid asymptotic approximations of the solution of hyperbolic systems of equations is presented. The averaged system of equations disintegrates into independent equations for non-resonance systems.…
We consider a nonlinear optical system in general, and a broad aperture laser in particular in a resonator where the diffraction coefficients are of opposite signs along two transverse directions. The system is described by the hyperbolic…
We present new methods to construct a Ruelle-Pollicott spectrum for the geodesic flow on manifolds with strictly negative curvature and a finite number of hyperbolic cusps.
The aim of this paper is to derive a formula for the subwavelength resonance frequency of an encapsulated bubble with arbitrary shape in two dimensions. Using Gohberg-Sigal theory, we derive an asymptotic formula for this resonance…
We use a combinatorial approximation of the hyperbolic plane to investigate properties of hyperbolic geometry such as exponential growth of perimeter and area of disks, and the linear isoperimetric inequality. This calculations give a…
The conical function and its relativistic generalization can be viewed as eigenfunctions of the reduced 2-particle Hamiltonians of the hyperbolic Calogero-Moser system and its relativistic generalization. We prove new product formulas for…
Convex co-compact 3-dimensional hyperbolic manifolds are uniquely determined by the pleating measured lamination on the boundary of their convex core.
We consider the problem of finding the resonances of the Laplacian on truncated Riemannian cones. In a similar fashion to Cheeger--Taylor, we construct the resolvent and scattering matrix for the Laplacian on cones and truncated cones.…
The starting point of this paper is the computation of minimal hyperbolic polynomials of duals of cones arising from chordal sparsity patterns. From that, we investigate the relation between ranks of homogeneous cones and their minimal…
For a conformally compact manifold that is hyperbolic near infinity and of dimension $n+1$, we complete the proof of the optimal $O(r^{n+1})$ upper bound on the resonance counting function, correcting a mistake in the existing literature.…