Alpay, Daniel Colombo, Fabrizio Diki, Kamal Sabadini, Irene
Published in
Integral Equations and Operator Theory

In this paper we begin the study of Schur analysis and of de Branges–Rovnyak spaces in the framework of Fueter hyperholomorphic functions. The difference with other approaches is that we consider the class of functions spanned by Appell-like polynomials. This approach is very efficient from various points of view, for example in operator theory, an...

Hur, Injo Ong, Darren C.
Published in
Integral Equations and Operator Theory

The KdV hierarchy is a family of evolutions on a Schrödinger operator that preserves its spectrum. Canonical systems are a generalization of Schrödinger operators, that nevertheless share many features with Schrödinger operators. Since this is a very natural generalization, one would expect that it would also be straightforward to build a hierarchy...

Zelenko, Leonid
Published in
Integral Equations and Operator Theory

This work is a continuation of our previous paper (Zelenko in Appl Anal Optim 3(2):281–306, 2019), where for the Schrödinger operator H=-Δ+V(x)·\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-...

Helffer, B. Sjöstrand, J.
Published in
Integral Equations and Operator Theory

The purpose of this paper is to revisit the proof of the Gearhart–Prüss–Huang–Greiner theorem for a semigroup S(t), following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on ‖S(t)‖\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \...

Shi, Rui
Published in
Integral Equations and Operator Theory

An interesting result proved by Halmos in Hal (Michigan Mathematical Journal, 15, 215–223 (1968) is that the set of irreducible operators is dense in B(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsid...

Čučković, Željko
Published in
Integral Equations and Operator Theory

Let Ω⊂Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \subset {\mathbb {C}}^n$$\end{document} be a smooth bounded pseudoconvex domain and A2(Ω)\documentclass[1...

Ito, Kenichi Jensen, Arne
Published in
Integral Equations and Operator Theory

We present an explicit formula for the resolvent of the discrete Laplacian on the square lattice, and compute its asymptotic expansions around thresholds in low dimensions. As a by-product we obtain a closed formula for the fundamental solution to the discrete Laplacian. For the proofs we express the resolvent in a general dimension in terms of the...

Gubkin, Pavel
Published in
Integral Equations and Operator Theory

We prove the Cesàro boundedness of eigenfunctions of the Dirac operator on the half-line with a square-summable potential. The proof is based on the theory of Krein systems and, in particular, on the continuous version of a theorem by A. Máté, P. Nevai and V. Totik from 1991.

Dziubański, Jacek Hejna, Agnieszka
Published in
Integral Equations and Operator Theory

On the Euclidean space RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}^N$$\end{document} equipped with a normalized root system R, a multiplicity functi...

Trostorff, Sascha Waurick, Marcus
Published in
Integral Equations and Operator Theory

We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider time-dependent partial differential equations in an exponentially weighted Hilbert space. In passing, one est...