Related papers: Lifting to the spectral ball with interpolation
We characterize the essential spectrum of the plasmonic problem for polyhedra in $\mathbb{R}^3$. The description is particularly simple for convex polyhedra and permittivities $\epsilon < - 1$. The plasmonic problem is interpreted as a…
In this paper we introduce a new fix point iteration scheme for solving nonlinear electromagnetic scattering problems. The method is based on a spectral formulation of Maxwell's equations called the Bidirectional Pulse Propagation…
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlev\'e equation.
Let $k$ be an algebraically closed field of characteristic $p > 0$. We consider the problem of lifting $p$-cyclic covers of $\Proj_k$ as $p$-cyclic covers of the projective line over some DVR under the condition that the wild monodromy is…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representations. The Lyapunov order plays a crucial role in…
In this paper we address the problem of interpolating a spline developable patch bounded by a given spline curve and the first and the last rulings of the developable surface. In order to complete the boundary of the patch a second spline…
We consider the problem of interpolating a holomorphic family of nondegenerate holomorphic jets on C^n for n > 1, parametrized by points in a Stein manifold, by a holomorphic family of automorphisms of C^n. We show that under a suitable…
We show that trapezoids with identical Neumann spectra are congruent up to rigid motions of the plane. The proof is based on heat trace invariants and some new wave trace invariants associated to certain diffractive billiard trajectories.…
The inversion in the sphere or Kelvin transformation, which exchanges the radial coordinate for its inverse, is used as a guide to relate distinct electrostatic problems with dual features. The exact solution of some nontrivial problems are…
Following ideas by Beardon, Minda and Baribeau, Rivard, Wegert in the context of the complex Schwarz-Pick Lemma, we use iterated hyperbolic difference quotients to prove a quaternionic multipoint Schwarz-Pick Lemma, in the context of the…
We describe all proper holomorphic mappings of the symmetrized polydisc and study its geometric properties. We also apply the obtained results to the study of the spectral unit ball in $\MM_n(\CC^n)$.
This paper aims to show that there exist non-symmetry constraints which yield integrable Hamiltonian systems through nonlinearization of spectral problems of soliton systems, like symmetry constraints. Taking the AKNS spectral problem as an…
We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an…
This paper presents an iterative scheme that converges to the solution of a pseudo-monotone variational inequality problem in the setting of $\mathbb{R}^{n}$. Traditional methods often require projections onto the feasible set…
We show that under some natural conditions, we are able to lift an $n$-dimensional spectral resolution from one monotone $\sigma$-complete unital po-group into another one, when the first one is a $\sigma$-homomorphic image of the second…
We study the multiplier algebras $A(\mathcal{H})$ obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces $\mathcal{H}$ on the ball $\mathbb{B}_d$ of $\mathbb{C}^d$. Our results apply, in particular, to the…
This paper presents an algorithmic study of a class of covering mixed-integer linear programming problems which encompasses classic cover problems, including multidimensional knapsack, facility location and supplier selection problems. We…
The algebraic geometric approach to $N$-component systems of nonlinear integrable PDE's is used to obtain and analyze explicit solutions of the coupled KdV and Dym equations. Detailed analysis of soliton fission, kink to anti-kink…
Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be the Blaschke product whose zeros are the nodes of the problem. It is proved that if $\Pi$ belongs to a certain class of inner functions, then the extremal solutions of…