Alexander Pushnitski
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Alexander Pushnitski has a total of 37 co-authors. Here are the top co-authors by number of shared publications:
- Dimitri R. Yafaev
Univ Rennes, CNRS, IRMAR UMR 6625, F-35000 Rennes, France
15 shared publications - Patrick Gérard
Université Paris-Saclay, Orsay, France
15 shared publications - Rupert L. Frank
Ludwig-Maximilians Universität München, Germany
7 shared publications - Karl-Mikael Perfekt
Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
5 shared publications - Grigori Rozenblum
Chalmers University of Technology, Gothenburg, Sweden
4 shared publications - Sergei Treil
Department of Mathematics, Brown University, Providence, RI, USA
4 shared publications
Latest Publications
- Open Access
Schrödinger operators on the half-line with integrable complex potentials
In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schrödinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In this paper, we study the case of $q \in L^1(\mathbb{R}_+)$. We derive explicit formulas for the spectral pair in terms of the Jost solutions of a system of two equations naturally associated with the non-self-adjoint Schrödinger operator. A key component of our work, which is of independent interest, is the existence proof and analysis of these Jost solutions.Open AccessSchrödinger operators on the half-line with integrable complex potentials
In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schrödinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In this paper, we study the case of $q \in L^1(\mathbb{R}_+)$. We derive explicit formulas for the spectral pair in terms of the Jost solutions of a system of two equations naturally associated with the non-self-adjoint Schrödinger operator. A key component of our work, which is of independent interest, is the existence proof and analysis of these Jost solutions. - Open Access
Ergodic Hankel operators
We introduce a new class of operators: ergodic families of self-adjoint Hankel operators realised as integral operators on the half-line. Inspired by the spectral theory of differential and finite-difference operators with ergodic coefficients, we develop a spectral theory of ergodic Hankel operators. For these operators, we define the Integrated Density of States (IDS) measure and establish its fundamental properties. In particular, we determine the total mass of the IDS measure in the positive semi-definite case. We also consider in more detail two classes of ergodic Hankel operators for which we are able to make further progress: periodic Hankel operators and the random Kronig--Penney--Hankel (rKPH) model. For periodic Hankel operators, we prove that the IDS measure is a sum of a pure point and absolutely continuous components, and describe the structure of both components. For the rKPH model, we prove the counterparts of the cornerstone results of the spectral theory of random Schrödinger operators: Lifshitz tails at the edges of the spectrum, the Wegner bound and Anderson localisation in a natural asymptotic regime. We conclude with some open problems.
Open AccessErgodic Hankel operators
We introduce a new class of operators: ergodic families of self-adjoint Hankel operators realised as integral operators on the half-line. Inspired by the spectral theory of differential and finite-difference operators with ergodic coefficients, we develop a spectral theory of ergodic Hankel operators. For these operators, we define the Integrated Density of States (IDS) measure and establish its fundamental properties. In particular, we determine the total mass of the IDS measure in the positive semi-definite case. We also consider in more detail two classes of ergodic Hankel operators for which we are able to make further progress: periodic Hankel operators and the random Kronig--Penney--Hankel (rKPH) model. For periodic Hankel operators, we prove that the IDS measure is a sum of a pure point and absolutely continuous components, and describe the structure of both components. For the rKPH model, we prove the counterparts of the cornerstone results of the spectral theory of random Schrödinger operators: Lifshitz tails at the edges of the spectrum, the Wegner bound and Anderson localisation in a natural asymptotic regime. We conclude with some open problems.
- 1 September 2025
- Published by Pleiades Publishing Ltd in Functional Analysis and Its Applications
- Vol. 59 (3) , 297-320
Unbounded Integral Hankel Operators
For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.
- 1 September 2025
- Published by Pleiades Publishing Ltd in Functional Analysis and Its Applications
- Vol. 59 (3) , 297-320
Unbounded Integral Hankel Operators
For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.
- Open Access
Unbounded integral Hankel operators
For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.
Open AccessUnbounded integral Hankel operators
For a wide class of unbounded integral Hankel operators on the positive half-line, we prove essential self-adjointness on the set of smooth compactly supported functions.
- 19 December 2024
- Published by Springer Nature in Journal d'Analyse Mathématique
- Vol. 154 (1) , 333-400
An inverse spectral problem for non-compact Hankel operators with simple spectrum
- 19 December 2024
- Published by Springer Nature in Journal d'Analyse Mathématique
- Vol. 154 (1) , 333-400
An inverse spectral problem for non-compact Hankel operators with simple spectrum
- Top Cited Papers
- 1 July 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (7) , 1-31
The Cubic Szegő Equation on the Real Line: Explicit Formula and Well-Posedness on the Hardy Class
- 1 July 2024
- Published by Springer Nature in Communications in Mathematical Physics
- Vol. 405 (7) , 1-31
Top Cited PapersThe Cubic Szegő Equation on the Real Line: Explicit Formula and Well-Posedness on the Hardy Class
- Open Access
- 13 June 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of Spectral Theory
- Vol. 14 (2) , 397-426
Editors’ introduction
Fritz Gesztesy, Ari Laptev, Alexander Pushnitski, Eugene Shargorodsky, Barry Simon
- 13 June 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of Spectral Theory
- Vol. 14 (2) , 397-426
Open AccessEditors’ introduction
Fritz Gesztesy, Ari Laptev, Alexander Pushnitski, Eugene Shargorodsky, Barry Simon
- 30 April 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 27 (11) , 4591-4648
An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line
We construct inverse spectral theory for finite rank Hankel operators acting on the Hardy space of the upper half-plane. A particular feature of our theory is that we completely characterise the set of spectral data. As an application of this theory, we prove the genericity of turbulent solutions of the cubic Szegő equation on the real line.
- 30 April 2024
- Published by European Mathematical Society - EMS - Publishing House GmbH in Journal of the European Mathematical Society
- Vol. 27 (11) , 4591-4648
An inverse problem for Hankel operators and turbulent solutions of the cubic Szegő equation on the line
We construct inverse spectral theory for finite rank Hankel operators acting on the Hardy space of the upper half-plane. A particular feature of our theory is that we completely characterise the set of spectral data. As an application of this theory, we prove the genericity of turbulent solutions of the cubic Szegő equation on the real line.
- 21 February 2024
- Published by Elsevier in Expositiones Mathematicae
- Vol. 42 (2)
Three families of matrices
- 21 February 2024
- Published by Elsevier in Expositiones Mathematicae
- Vol. 42 (2)
Three families of matrices
- Open Access
Three families of matrices
This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that they can be understood as matrices of some linear operations on appropriate Hardy spaces.
Open AccessThree families of matrices
This paper has an expository nature. We compare the spectral properties (such as boundedness and compactness) of three families of semi-infinite matrices and point out similarities between them. The common feature of these families is that they can be understood as matrices of some linear operations on appropriate Hardy spaces.