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Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

Analysis of PDEs · Mathematics 2021-07-06 Thomas Krainer

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…

Classical Analysis and ODEs · Mathematics 2007-05-23 Joseph A. Ball , Vladimir Bolotnikov , Quanlei Fang

Let $g$ be a finite dimensional real Lie algebra. Let $r:g\to End(V)$ be a representation of $g$ in a finite dimensional real vector space. Let $C_{V}=(End(V)\tens S(g))^{g}$ be the algebra of $End(V)$-valued invariant differential…

Representation Theory · Mathematics 2007-05-23 Pascal Lavaud

We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence are imposed on certain components of the subgrading. This allows us to obtain some useful information about the…

Operator Algebras · Mathematics 2010-01-20 Matthew Kennedy , Victor Shulman , Yuri Turovskii

We revisit the work of Rieffel and van Daele on pairs of subspaces of a real Hilbert space, while relaxing as much as possible the assumption that all the relevant subspaces are in general positions with respect to each other. We work out,…

Mathematical Physics · Physics 2025-03-10 Jan Naudts , Jun Zhang

We characterize the bounded and compact generalized Volterra companion integral operators on Fock spaces acting between the standard Fock spaces. As a special case, we prove that there exist no nontrivial compact Volterra companion integral…

Complex Variables · Mathematics 2015-05-28 Tesfa Mengestie

We study the generalized Volterra-type integral and composition operators acting on the classical Fock spaces. We first characterize various properties of the operators in terms of growth and integrability conditions which are simpler to…

Functional Analysis · Mathematics 2018-02-26 Tesfa Mengestie , Mafuz Worku

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…

Exactly Solvable and Integrable Systems · Physics 2023-04-07 P. Prakash , K. S. Priyendhu , M. Lakshmanan

In this article, we completely classify invariant subspaces of finite-rank perturbations of a class of Toeplitz operators on vector-valued Hardy spaces. As a consequence, in the vector-valued setting, we characterize invariant and almost…

Functional Analysis · Mathematics 2026-02-25 Arshad Khan , Sneh Lata , Dinesh Singh

Let $S_{E}$ be the shift operator on vector-valued Hardy space $H_{E}^{2}.$ Beurling-Lax-Halmos Theorem identifies the invariant subspaces of $S_{E}$ and hence also the invariant subspaces of the backward shift $S_{E}^{\ast}.$ In this…

Functional Analysis · Mathematics 2023-09-25 Caixing Gu , Shuaibing Luo

The inverse nodal problem for Dirac differential operator perturbated by a Volterra integral operator is studied. We prove that dense subset of the nodal points determines the coefficients of differential and integral part of the operator.…

Spectral Theory · Mathematics 2016-06-30 Baki Keskin , A. Sinan Ozkan

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In…

Functional Analysis · Mathematics 2015-06-26 Farrukh Mukhamedov , Hasan Akin , Seyit Temir

We characterise narrow and strong Daugavet operators on $C(K,E)$-spaces; these are in a way the largest sensible classes of operators for which the norm equation $\|Id+T\| = 1+\|T\|$ is valid. For certain separable range spaces $E$…

Functional Analysis · Mathematics 2011-03-17 Dmitriy Bilik , Vladimir Kadets , Roman Shvidkoy , Gleb Sirotkin , Dirk Werner

We prove that if T is an operator on an infinite-dimensional Hilbert space whose spectrum and essential spectrum are both connected and whose Fredholm index is only 0 or 1, then the only nontrivial norm-stable invariant subspaces of T are…

Functional Analysis · Mathematics 2010-08-20 Alexander Borichev , Don Hadwin , Hassan Yousefi

The techniques developed by Popescu, Muhly-Solel and Good for the study of algebras generated by weighted shifts are applied to generalize results of Sarkar and of Bhattacharjee-Eschmeier-Keshari-Sarkar concerning dilations and invariant…

Functional Analysis · Mathematics 2020-03-10 Baruch Solel

The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel\'{a}ez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for…

Functional Analysis · Mathematics 2020-09-22 Qingze Lin

We discuss the concept of invariant subspaces for unbounded linear operators, point out some shortcomings of known definitions, and propose our own.

Functional Analysis · Mathematics 2025-05-13 M. I. Belishev , S. A. Simonov

We study the boundedness and compactness of the generalized Volterra integral operator on weighted Bergman spaces with doubling weights on the unit disk. A generalized Toeplitz operator is defined and the boundedness, compactness and…

Complex Variables · Mathematics 2021-09-03 Juntao Du , Songxiao Li , Dan Qu

In this paper invariant subspace method has been employed for solving linear and non-linear fractional partial differential equations involving Caputo derivative. A variety of illustrative examples are solved to demonstrate the…

Analysis of PDEs · Mathematics 2017-04-18 Sangita Choudhary , Varsha Daftardar-Gejji

We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems…

Complex Variables · Mathematics 2015-07-16 Tesfa Mengestie