On matrix–valued Herglotz functions

F Gesztesy, E Tsekanovskii - Mathematische Nachrichten, 2000 - Wiley Online Library
We provide a comprehensive analysis of matrix–valued Herglotz functions and illustrate
their applications in the spectral theory of self–adjoint Hamiltonian systems including matrix …

Partial Inverse Sturm-Liouville Problems

NP Bondarenko - Mathematics, 2023 - mdpi.com
This paper presents a review of both classical and modern results pertaining to partial
inverse spectral problems for differential operators. Such problems consist in the recovery of …

A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure

F Gesztesy, B Simon - Annals of mathematics, 2000 - JSTOR
We continue the study of the A-amplitude associated to a half-line Schrodinger operator,-
d2/dx2+ q in L2 ((0, b)), b≤∞. A is related to the Weyl-Titchmarsh m-function via m (-κ2)=-κ …

Weyl–Titchmarsh 𝑀-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators

S Clark, F Gesztesy - Transactions of the American Mathematical Society, 2002 - ams.org
We explicitly determine the high-energy asymptotics for Weyl–Titchmarsh matrices
associated with general Dirac-type operators on half-lines and on $\mathbb {R} $. We also …

Inverse spectral problems for Dirac operators with summable potentials

S Albeverio, R Hryniv, Y Mykytyuk - arXiv preprint math/0701158, 2007 - arxiv.org
The spectral properties of Dirac operators on $(0, 1) $ with potentials that belong entrywise
to $ L_p (0, 1) $, for some $ p\in [1,\infty) $, are studied. The algorithm of reconstruction of the …

Uniqueness results for matrix‐valued Schrödinger, Jacobi, and Dirac‐type operators

F Gesztesy, A Kiselev… - Mathematische …, 2002 - Wiley Online Library
Uniqueness Results for Matrix╒Valued Schrödinger, Jacobi, and Dirac╒Type Operators
Page 1 Math. Nachr. 239-240 (2002), 103 – 145 Uniqueness Results for Matrix–Valued …

[HTML][HTML] On the Riesz basis property of root vectors system for 2× 2 Dirac type operators

AA Lunyov, MM Malamud - Journal of Mathematical Analysis and …, 2016 - Elsevier
The paper is concerned with the Riesz basis property of a boundary value problem
associated in L 2 [0, 1]⊗ C 2 with the following 2× 2 Dirac type equation (0.1) L y=− i B− 1 …

On the completeness of root subspaces of boundary value problems for first order systems of ordinary differential equations

MM Malamud, LL Oridoroga - Journal of Functional Analysis, 2012 - Elsevier
The paper is concerned with the completeness problem of root functions of general
boundary value problems for first order systems of ordinary differential equations. We …

Asymptotic analysis of solutions of ordinary differential equations with distribution coefficients

AM Savchuk, AA Shkalikov - Sbornik: Mathematics, 2020 - iopscience.iop.org
Asymptotic analysis of solutions of ordinary differential equations with distribution
coefficients - IOPscience This site uses cookies. By continuing to use this site you agree to …

Half-inverse problem for diffusion operators on the finite interval

H Koyunbakan, ES Panakhov - Journal of Mathematical Analysis and …, 2007 - Elsevier
The potential function q (x) in the regular and singular Sturm–Liouville problem can be
uniquely determined from two spectra. Inverse problem for diffusion operator given at the …