Published in Advances in Operator Theory
In this paper, we prove an extension of the Helson–Lowdenslager theorem for L2(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {L}^2(\mathbb {T})$$\end{docum...
Published in Annals of Functional Analysis
We obtain a Shimorin Wold-type decomposition for a doubly commuting covariant representation of a product system of C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^...
Published in Advances in Operator Theory
We study the existence of renormalized solutions to a nonlinear parabolic boundary value problem with a general and possibly singular measure data, whose model is (P)∂b(u)∂t-Δp(x)u=μinQ:=Ω×(0,T),b(u)(t=0)=b(u0)(x)inΩ,u(x,t)=0on∂Ω×(0,T),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}...
Published in Advances in Operator Theory
Recently, Liang and Partington (Integr Equ Oper Theory 92(4): 35, 2020) show that kernels of finite-rank perturbations of Toeplitz operators are nearly invariant with finite defect under the backward shift operator acting on the scalar-valued Hardy space. In this article, we provide a vectorial generalization of a result of Liang and Partington. As...
Published in Integral Equations and Operator Theory
Tensor product of Fock spaces is analogous to the Hardy space over the unit polydisc. This plays an important role in the development of noncommutative operator theory and function theory in the sense of noncommutative polydomains and noncommutative varieties. In this paper we study joint invariant subspaces of tensor product of full Fock spaces an...
Published in Sampling Theory, Signal Processing, and Data Analysis
In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of L2(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{doc...
Published in Results in Mathematics
This article studies a type of integrable linear ordinary differential equations considered by Shifner [17] and generalised by Erougin [5], Salakhova and Chebotarev [15]. We will consider a slight generalisation of their results.
Published in Integral Equations and Operator Theory
The paper deals with bounded linear operators T on a complex Hilbert space H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}$$\end{document} which have 2-...
In this article we first obtain an asymptotic expression of the $N+1$ eigenvalues of the Toeplitz matrix $T_N(f)$ where $f$ is a strictly increasing or strictly decreasing, differentiable and even function on $[-\pi,\pi]$. In the particular case where the symbol only verifies these assumptions locally we specify the eigenvalues that belong to a cer...
Finite rank perturbations $T=N+K$ of a bounded normal operator $N$ on a separable Hilbert space are studied thanks to a natural functional model of $T$; in its turn the functional model solely relies on a perturbation matrix/ characteristic function previously defined by the second author. Function theoretic features of this perturbation matrix enc...
