The half-inverse spectral problem for a Sturm–Liouville operator consists in reconstruction of
this operator from its spectrum and half of the potential. We give the necessary and sufficient …

Vibrating strings and the sound they generate have fascinated humankind ever since homo
sapiens inhabited the earth, and almost every culture has constructed musical string …

We consider one-dimensional Dirac operator LP, U with Birkhoff regular boundary
conditions and summable potential P (x) on [0, π]. We introduce strongly and weakly regular …

We solve two inverse spectral problems for star graphs of Stieltjes strings with Dirichlet and
Neumann boundary conditions, respectively, at a selected vertex called root. The root is …

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 …

By using quasi--derivatives we develop a Fourier method for studying the spectral gaps of
one dimensional Schr\" odinger operators with periodic singular potentials $ v. $ Our results …

In this paper, we give a reduction formula for the characteristic functions of the Sturm–
Liouville boundary value problems defined on a tree. We also discuss the multiplicity of the …

Inverse spectral problems for Sturm–Liouville operators in impedance form Page 1 Journal of
Functional Analysis 222 (2005) 143–177 www.elsevier.com/locate/jfa Inverse spectral …

The three-spectral inverse problem for a Stieltjes string (a thread bearing finite number of
point masses) is solved. The inverse problem for a Stieltjes string damped at an interior point …

This paper is motivated by a problem in mechanics, where the density of a string subject to
various constraints needs to be determined from the frequencies of the string's oscillations …