Related papers: Riemann-Hilbert problem for Hurwitz Frobenius mani…
We consider the inverse problem of recovering the magnetic and potential term of a magnetic Schr\"{o}dinger operator on certain compact Riemannian manifolds with boundary from partial Dirichlet and Neumann data on suitable subsets of the…
In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to…
We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities…
Commutative Hilbertian Frobenius algebras are those commutative semi-group objects in the monoidal category of Hilbert spaces, for which the Hilbert adjoint of the multiplication satisfies the Frobenius compatibility relation, that is, this…
In this paper a twofold inverse problem for orthogonal matrix functions in the Wiener class is considered. The scalar-valued version of this problem was solved by Ellis and Gohberg in 1992. Under reasonable conditions, the problem is…
We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…
This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schr\"{o}dinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order…
Inverse problems arising in (geo)magnetism are typically ill-posed, in particular {they exhibit non-uniqueness}. Nevertheless, there exist nontrivial model spaces on which the problem is uniquely solvable. Our goal is here to describe such…
The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be…
We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule, described in a companion paper.…
We will give an explicit construction of the invariant Hermitian form for the monodromy of an $A$-hypergeometric system given that there is a Mellin-Barnes basis of solutions.
We characterize the biorthogonal polynomials that appear in the theory of coupled random matrices via a Riemann-Hilbert problem. Our Riemann-Hilbert problem is different from the ones that were proposed recently by Ercolani and McLaughlin,…
We consider the dynamic problems for the discrete systems with discrete time associated with finite and semi-infinite Jacobi matrices. The result of the paper is a procedure of association of special Hilbert spaces of functions, namely de…
In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational…
This paper is concerned with the inverse problem of constructing a symmetric nonnegative matrix from realizable spectrum. We reformulate the inverse problem as an underdetermined nonlinear matrix equation over a Riemannian product manifold.…
The vector Riemann-Hilbert problem is analyzed when the entries of its matrix coefficient are meromorphic and almost periodic functions. Three cases for the meromorphic functions, when they have (i) a finite number of poles and zeros…
We analyze convergence of the Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. Specifically, we establish local convergence and convergence rates for a class of inverse problems that satisfy H\"{o}lder…
A parabolic partial differential equation $u'_t(t,x)=Lu(t,x)$ is considered, where $L$ is a linear second-order differential operator with time-independent coefficients, which may depend on $x$. We assume that the spatial coordinate $x$…
Moduli spaces of algebraic curves and closely related to them Hurwitz spaces, that is, spaces of meromorphic functions on the curves, arise naturally in numerous problems of algebraic geometry and mathematical physics, especially in…
We prove that the holomorphic solutions of Picard-Fuchs differential equations associated with one-parameter families of abelian varieties with real multiplication admit power series expansions with $S$-integral coefficients at a maximal…