Related papers: Singularities of the wave trace for the Friedlande…
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e…
A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…
We give a formula to count the number of $D_4$ singularities in a stable frontal perturbation of a corank $2$ wave front singularity $f\colon (\mathbb{C}^3,0) \to (\mathbb{C}^4,0)$ using Mond's method of stable perturbations of map germs.…
We derive contributions to the trace formula for the spectral density accounting for the role of diffractive orbits in two-dimensional billiard systems with corners. This is achieved by using the exact Sommerfeld solution for the Green…
We study a nonlinear wave for a system of balance laws in one space dimension, which describes combustion for two-phase (gas and liquid) flow in porous medium. The problem is formulated for a general $N$-component liquid for modeling the…
In this paper we are interested on the well-posedness of Dirichlet problems associated to integro-differential elliptic operators of order $\alpha < 1$ in a bounded smooth domain $\Omega$ . The main difficulty arises because of losses of…
The family of circular Jacobi $\beta$ ensembles has a singularity of a type associated with Fisher and Hartwig in the theory of Toeplitz determinants. Our interest is in the Fourier transform of the corresponding bulk scaled spectral…
A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $\alpha$-multiple of the Dirac $\delta$-type damping, is derived. Depending on the choice of the…
In this paper we define and analyze singularities of discrete linear Weingarten surfaces with Weierstrass-type representations in $3$-dimensional Riemannian and Lorentzian spaceforms. In particular, we discuss singularities of discrete…
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
This paper is part I of a series in which we aim to show that the singular support of the wave trace and the length spectrum of a smooth, strictly convex, and bounded planar billiard table are generally distinct objects. We derive an…
The formation of singularities in the three-dimensional Euler equation is investigated. This is done by restricting the number of Fourier modes to a set which allows only for local interactions in wave number space. Starting from an initial…
For distinct unitary cuspidal automorphic representations $\pi_1$ and $\pi_2$ for $\mathrm{GL}(2)$ over a number field $F$ and any $\alpha\in\Bbb{R}$, let $\mathcal{S}_{\alpha}$ be the set of primes $v$ of $F$ for which…
Unique continuation principles are fundamental properties of elliptic partial differential equations, giving conditions that guarantee that the solution to an elliptic equation must be uniformly zero. Since finite-element discretizations…
In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…
We show uniqueness for overdetermined elliptic problems defined on topological disks $\Omega$ with $C^2$ boundary, i.e., positive solutions $u$ to $\Delta u + f(u)=0$ in $\Omega \subset (M^2,g)$ so that $u = 0$ and $\frac{\partial…
We continue the study of the analogue of Thurston's metric on the Teichm{\"u}ller space of Euclidean triangle which was started by Saglam and Papadopoulos in [1].By direct calculation, we give explicit expressions of the distance function…
We consider the spectral Dirichlet problem for the Laplace operator in the plane $\Omega^{\circ}$ with double-periodic perforation but also in the domain $\Omega^{\bullet}$ with a semi-infinite foreign inclusion so that the Floquet-Bloch…
In this note we study the problem of evaluating the trace of $f(T)-f(R)$, where $T$ and $R$ are contractions on Hilbert space with trace class difference, i.e., $T-R\in\boldsymbol{S}_1$ and $f$ is a function analytic in the unit disk ${\Bbb…
Let $P$ be a $\delta$-separated $(\delta, s, C_P)$-set of points in $B(0, 1)\subset \mathbb{R}^d$ and $\Pi$ be a $\delta$-separated $(\delta, t, C_\Pi)$-set of hyperplanes intersecting $B(0, 1)$ in $\mathbb{R}^d$. Define \[I_{C\delta}(P,…