7 citations · 14 across the 16 of their papers we have counts for
19 papers
Scattering of plane waves and a modified Pompeiu criterion
Narek Hovsepyan, Michael S. Vogelius
In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introductio…
Higher-order necessary conditions for nonscattering
Narek Hovsepyan
We study the scattering of incident waves by a class of planar analytic inhomogeneities with constant refractive index, governed by the Helmholtz equation. We derive an infinite hi…
On the potential lack of response in a model of second-harmonic generation. A computer-assisted proof
Miguel Ayala, Dominic Blanco, Fioralba Cakoni +2
This paper provides a rigorous computer-assisted proof of the existence of generalized transmission eigenvalues arising in nonlinear optics in the context of high-order harmonic ge…
Scattering of plane waves
Narek Hovsepyan, Michael S. Vogelius
We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz e…
Scattering from analytic and piecewise analytic inhomogeneities
Narek Hovsepyan, Michael S. Vogelius
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regula…
On the lack of external response of a nonlinear medium in the second-harmonic generation process
Fioralba Cakoni, Narek Hovsepyan, Matti Lassas +1
This paper concerns the scattering problem for a nonlinear medium of compact support, , with second-harmonic generation. Such a medium, when probed with monochromatic light beam…
Far field broadband approximate cloaking for the Helmholtz equation with a Drude-Lorentz refractive index
Fioralba Cakoni, Narek Hovsepyan, Michael Vogelius
This paper concerns the analysis of a passive, broadband approximate cloaking scheme for the Helmholtz equation in for or . Using ideas from transformati…
On the distribution of Born transmission eigenvalues in the complex plane
Narek Hovsepyan
We analyze an approximate interior transmission eigenvalue problem in for or , motivated by the transmission problem of a transformation optics-based clo…
On the commutation properties of finite convolution and differential operators I: commutation
Yury Grabovsky, Narek Hovsepyan
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete…
On the optimal analytic continuation from discrete data
Narek Hovsepyan
We consider analytic functions from a reproducing kernel Hilbert space. Given that such a function is of order on a set of discrete data points, relative to its global size, we…
On the extreme rays of the cone of quasiconvex quadratic forms: Extremal determinats vs extremal and polyconvex forms
Davit Harutyunyan, Narek Hovsepyan
This work is concerned with the study of the extreme rays of the convex cone of quasiconvex quadratic forms (denoted by ). We characterize quadratic forms $…
On feasibility of extrapolation of the complex electromagnetic permittivity function using Kramer-Kronig relations
Yury Grabovsky, Narek Hovsepyan
We study the degree of reliability of extrapolation of complex electromagnetic permittivity functions based on their analyticity properties. Given two analytic functions, represent…
Rigidity of a thin domain depends on the curvature, width, and boundary conditions
Zhirayr Avetisyan, Davit Harutyunyan, Narek Hovsepyan
This paper is concerned with the study of linear geometric rigidity of shallow thin domains under zero Dirichlet boundary conditions on the displacement field on the thin edge of t…
Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces
Yury Grabovsky, Narek Hovsepyan
The need for analytic continuation arises frequently in the context of inverse problems. Notwithstanding the uniqueness theorems, such problems are notoriously ill-posed without ad…
On the commutation properties of finite convolution and differential operators II: sesquicommutation
Yury Grabovsky, Narek Hovsepyan
We introduce and fully analyze a new commutation relation between finite convolution integral operator and differential operators and ,…
Analytic continuation in an annulus and in a Bernstein ellipse
Yury Grabovsky, Narek Hovsepyan
Analytic continuation problems are notoriously ill-posed without additional regularizing constraints, even though every analytic function has a rigidity property of unique continua…
Optimal error estimates for analytic continuation in the upper half-plane
Yury Grabovsky, Narek Hovsepyan
Analytic functions in the Hardy class over the upper half-plane are uniquely determined by their values on any curve lying in the interior or on the bounda…
Hopf Bifurcation in Structural Population Models
Narek Hovsepyan, Juan J. L. Velázquez
We study a nonlinear PDE problem motivated by the peculiar patterns arising in myxobacteria, namely counter-migrating cell density waves. We rigorously prove the existence of Hopf…
On the commutation properties of finite convolution and differential operators I: commutation
Yury Grabovsky, Narek Hovsepyan
The commutation relation between finite convolution integral operator and differential operator has implications for spectral properties of . We characterize a…