A method of ascent for solving boundary value problems

Determination of a differential pencil from interior spectral data

“…Inverse problems of spectral analysis involve reconstruction of a linear operator from its spectral characteristics [1,3,[8][9][10][20][21][22]25]. For inverse SturmLiouville problems, such characteristics are two spectra for different boundary conditions, one spectrum and normalizing constants, spectral functions, nodal points (zeros of eigenfunctions) as given spectral data, scattering data, the Weyl function [3][4][5][6][8][9][10][11][12][13][14][15][16]18,23,[27][28][29]31]. Such problems play an important role in mathematics and have many applications in natural sciences.…”

On impulsive Sturm–Liouville operators with Coulomb potential and spectral parameter linearly contained in boundary conditions

“…Since 1946, various forms of the inverse problem have been considered by numerous authors (Borg [15], Levinson [8], Levitan [9], etc. ), and there now exists an extensive literature on this topic (see [10][11][12][13][14]). Later, inverse problems having specified singularities were considered by a number of authors (see [18][19][20]).…”

Inverse spectral problems for the Sturm–Liouville operator on a d-star graph

“…Spectral and scattering properties of Schrödinger operator in such structures attracted a considerable attention during past years. There exists an extensive literature devoted to inverse spectral problems for ordinary differential operators on a finite interval; we mention only the literature [2,4,[6][7][8][9][10][11][12]16,[20][21][22]. Recently, the spectral problems of quantum graphs have become a rapidly-developing field of mathematics and mathematical physics, and spectral properties of quantum graphs and different inverse problems have been studied in both forward [13,17,24] and inverse [1,3,5,14,18,19,23,[25][26][27][28], etc.…”