Related papers: Global transformations preserving spectral data
Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…
This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…
In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville…
A method for solving spectral problems for the Sturm-Liouville equation $(pv^{\prime})^{\prime}-qv+\lambda rv=0$ based on the approximation of the Delsarte transmutation operators combined with the Liouville transformation is presented. The…
The classical Calder\'on problem with partial data is known to be log-log stable in some special cases, but even the uniqueness problem is open in general. We study the partial data stability of an analogous inverse fractional conductivity…
In this paper, we investigate the global existence of spherically symmetric strong solutions with large initial data to an initial-boundary value problem of the multidimensional isentropic compressible Navier-Stokes-Korteweg system in an…
The operator of double differentiation, perturbed by the composition of the differentiation operator and a convolution one, on a finite interval with Dirichlet boundary conditions is considered. We obtain uniform stability of recovering the…
We study the inverse Sturm-Liouville problem on a finite interval from partial knowledge of spectral data. Specifically, we show that the potential can be uniquely reconstructed from the knowledge of a fraction of Dirichlet eigenvalues…
Liouville transformations of Schr\"odinger equations preserve the scattering amplitudes while changing the effective potential. We discuss the properties of these gauge transformations and introduce a special Liouville gauge which allows…
We outline a new method of construction of global-in-time weak solutions of the Liouville equation - and also of the associated BBGKY hierarchy - corresponding to the hard sphere singular Hamiltonian. Our method makes use only of geometric…
For each $f\!:\!\mathbb{R}\to\mathbb{C}$ that is Henstock--Kurzweil integrable on the real line, or is a distribution in the completion of the space of Henstock--Kurzweil integrable functions in the Alexiewicz norm, it is shown that the…
We discuss inverse spectral theory for singular differential operators on arbitrary intervals $(a,b) \subseteq \mathbb{R}$ associated with rather general differential expressions of the type \[\tau f = \frac{1}{r} \left(- \big(p[f' + s…
In this paper, we prove the following result. Let $\alpha$ be any real number between $0$ and $2$. Assume that $u$ is a solution of $$ \left\{\begin{array}{ll} (-\Delta)^{\alpha/2} u(x) = 0 , \;\; x \in \mathbb{R}^n ,\\…
We study nonnegative solutions to the following Hardy-H\'enon type equations involving higher order fractional Laplacians $$ (-\Delta)^\sigma u = |x|^{-\alpha}u^{p} ~~~~~~ \mbox{in} ~ \mathbb{R}^n \backslash \{0\} $$ with a possible…
We study characteristic functions and describe asymptotics of the eigenvalues for the spectral Sturm-Liouville problem on graphs equipped with Robin-Kirhhoff boundary conditions. Also, we show how to recover the coefficients in the Robin…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
Given a two--dimensional mapping $U$ whose components solve a divergence structure elliptic equation, we give necessary and sufficient conditions on the boundary so that $U$ is a global diffeomorphism.
We discuss the problem of the inverse spectral problem of Sturm-Liouville operator with multiple frozen arguments at $\{a_{1}, a_{2},\ldots,a_{N}\}$ in $(0,\pi)$. One may consider the characteristic functions as perturbation of sine or of…
Uniform convergence of the expansion of an absolutely continuous function for eigenfunctions of the Sturm-Liouville problem $-y" + q \left( x \right) y = \mu y,$ $y \left(0\right)=0,$ $y\left( \pi \right)\cos \beta + y'\left( \pi…
We consider two main inverse Sturm-Liouville problems: the problem of recovery of the potential and the boundary conditions from two spectra or from a spectral density function. A simple method for practical solution of such problems is…