Related papers: An Uniqueness Result on Spherically Stratified Med…
In the paper we propose a direct method for recovering the Sturm-Liouville potential from the Weyl-Titchmarsh $m$-function given on a countable set of points. We show that using the Fourier-Legendre series expansion of the transmutation…
The representations of the kernels of the transmutation operator and of its inverse relating the one-dimensional Schr\"odinger operator with the second derivative are obtained in terms of the eigenfunctions of a corresponding…
In this paper we prove some results on interior transmission eigenvalues. First, under rea- sonable assumptions, we prove that the spectrum is a discrete countable set and the generalized eigenfunctions spanned a dense space in the range of…
The impact of surface reflection on the statistics of transmission eigenvalues is a largely unexplored subject of fundamental and practical importance in statistical optics. Here, we develop a first-principles theory and confirm numerically…
We look for best partitions of the unit interval that minimize certain functionals defined in terms of the eigenvalues of Sturm-Liouville problems. Via \Gamma-convergence theory, we study the asymptotic distribution of the minimizers as the…
We consider the interior transmission eigenvalue (ITE) problem, which arises when scattering by inhomogeneous media is studied. The ITE problem is not self-adjoint. We show that positive ITEs are observable together with plus or minus signs…
We consider inverse obstacle and transmission scattering problems where the source of the incident waves is located on a smooth closed surface that is a boundary of a domain located outside of the obstacle/inhomogeneity of the media. The…
We consider a second order functional-differential pencil with two constant delays of the argument and study the inverse problem of recovering its coefficients from the spectra of two boundary value problems with one common boundary…
We study an indefinite Sturm-Liouville problem due to Richardson whose complicated eigenvalue dependence on a parameter has been a puzzle for decades. In atomic physics a process exists that inverts the usual Schrodinger situation of an…
We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…
We suggest a new formulation of the inverse spectral problem for second-order functional-differential operators on star-shaped graphs with global delay. The latter means that the delay, being measured in the direction to a specific boundary…
Sturm-Liouville problem with generalized derivative of self-similar Cantor type function as a weight is considered. Under Neumann and mixed boundary conditions the oscillating properties of the eigenfunctions are studied. The spectral…
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…
Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…
In this study, a formula for regularized sums of eigenvalues of a Sturm-Liouville problem with retarded argument at the point of discontinuity is obtained. Moreover, oscillation properties of the related problem is investigated.
We give a brief overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS) and propose a new method for numerical solution of corresponding…
We consider the reflection-transmission problem in a waveguide with obstacle. At certain frequencies, for some incident waves, intensity is perfectly transmitted and the reflected field decays exponentially at infinity. In this work, we…
The eigenvalues of the transmission matrix provide the basis for a full description of the statistics of steady-state transmission and conductance. At the same time, the ability to excite the sample with the waveform of specific…
This paper deals with the Sturm-Liouville operators with distribution potentials of the space $W_2^{-1}$ on a metric tree. We study an inverse spectral problem that consists in the recovery of the potentials from the characteristic…
In this study, we consider a boundary value problem generated by the Sturm-Liouville problem with a frozen argument and with non-separated boundary conditions on a time scale. Firstly, we present some solutions and characteristic function…