Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials

J Eckhardt, F Gesztesy, R Nichols, G Teschl - arXiv preprint arXiv …, 2012 - arxiv.org
We systematically develop Weyl-Titchmarsh theory for singular differential operators on
arbitrary intervals $(a, b)\subseteq\mathbb {R} $ associated with rather general differential …

1-D Schrödinger operators with local point interactions: a review

A Kostenko, M Malamud - Spectral Analysis, Integrable Systems …, 2013 - books.google.com
We review recent developments in the theory of 1-D Schrödinger operators with local point
interactions on a discrete set. The progress in this area was stimulated by recent advances …

Linear differential operators with distribution coefficients of various singularity orders

NP Bondarenko - Mathematical Methods in the Applied …, 2023 - Wiley Online Library
In this paper, the linear differential expression of order n≥ 2 n ≥ 2 with distribution
coefficients of various singularity orders is considered. We obtain the associated matrix for …

[HTML][HTML] Reconstruction of higher-order differential operators by their spectral data

NP Bondarenko - Mathematics, 2022 - mdpi.com
This paper is concerned with inverse spectral problems for higher-order (n> 2) ordinary
differential operators. We develop an approach to the reconstruction from the spectral data …

[HTML][HTML] Inverse spectral problems for arbitrary-order differential operators with distribution coefficients

NP Bondarenko - Mathematics, 2021 - mdpi.com
In this paper, we propose an approach to inverse spectral problems for the n-th order (n≥ 2)
ordinary differential operators with distribution coefficients. The inverse problems which …

[HTML][HTML] Regularization and inverse spectral problems for differential operators with distribution coefficients

NP Bondarenko - Mathematics, 2023 - mdpi.com
In this paper, we consider a class of matrix functions that contains regularization matrices of
Mirzoev and Shkalikov for differential operators with distribution coefficients of order n≥ 2 …

[HTML][HTML] Local solvability and stability of an inverse spectral problem for higher-order differential operators

NP Bondarenko - Mathematics, 2023 - mdpi.com
In this paper, we, for the first time, prove the local solvability and stability of an inverse
spectral problem for higher-order (n> 3) differential operators with distribution coefficients …

On recovering quadratic pencils with singular coefficients and entire functions in the boundary conditions

M Kuznetsova - Mathematical Methods in the Applied Sciences, 2023 - Wiley Online Library
The paper deals with a new type of inverse spectral problems for second‐order quadratic
differential pencils when one of the boundary conditions involves arbitrary entire functions of …

Formally self-adjoint quasi-differential operators and boundary value problems

A Goriunov, V Mikhailets, K Pankrashkin - arXiv preprint arXiv:1205.1810, 2012 - arxiv.org
We develop the machinery of boundary triplets for one-dimensional operators generated by
formally self-adjoint quasi-differential expression of arbitrary order on a finite interval. The …

Inverse spectral theory for Sturm-Liouville operators with distributional potentials

J Eckhardt, F Gesztesy, R Nichols, G Teschl - arXiv preprint arXiv …, 2012 - arxiv.org
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 …