arXiv subjects

Jahangir Cheshmavar

Publications and source records attributed to Jahangir Cheshmavar.

10 recordsLinked to original sources

arXiv2026

Adaptive resolution frames: A multilevel framework in Hilbert spaces

We introduce adaptive resolution frames (AR-frames), a class of weighted frames equipped with a partitioned index structure that models multiple resolution levels in Hilbert spaces. We establish a block-triangular representation of the associated operators and prove the convergence of an iterative reconstruction method with explicit error estimates. We further derive optimal block-diagonal preconditioners that minimize the iteration error and obtain stability results showing that AR-frames and their canonical reconstruction operators remain stable under sufficiently small weighted perturbations. These results provide a unified framework for efficient reconstruction and perturbation analysis of AR-frames.

math.FA↗

arXiv2025

Frame properties induced by iteration of a multiplication operator on Hardy spaces

Motivated by the study of frame properties arising from iterates of linear operators, it was previously established that the multiplication operator $T_ϕx(t) = ϕ(t)x(t)$ cannot generate a frame in $L^2(a,b)$ (Results Math, 2019). In this note, we examine the behavior of such operators on the Hardy space $H^2(D)$, the Hilbert space of holomorphic functions on the open unit disk $D$ with square integrable boundary values. We show that, in contrast to the $L^2$-setting, the iterates of $T_ϕ$, for $ϕ\in H^{\infty}(D)$, exhibit fundamentally different frame properties in $H^2(D)$, leading to new structural insights and results.

math.FA↗

arXiv2024

Continuous $K$-$g$-frames in Hilbert $C^*$-modules

This study aims at combining the concepts of $g$-frame and $K$-frame for a Hilbert $C^*$-module $U$, for an operator $K \in End^*_A(U)$, where $End^*_A(U)$ contains all adjointable $A$-linear maps on $U$. As a result, continuous $K$-$g$-frames for Hilbert $C^*$-modules are introduced and studied. Subsequently, some characterizations of continuous $K$-$g$-frames in Hilbert $C^*$-modules are proved. Next, continuous $K$-$g$-dual of a $c$-$K$-$g$-frame is introduced. Finally, some results, particularly, the existence of continuous $K$-$g$-dual, are derived.

math.FA↗

arXiv2023

On abstract results of operator representation of frames in Hilbert spaces

In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that -- is a frame for H, for some -- . We state a necessary condition in order for a frame -- to have a representation of the form -- . Frame sequence -- with the synthesis operator U, have also been characterized in terms of the behavior spectrum of -- . Next, using the operator response of an element with respect to a unit vector in H, frames -- of the form -- are characterized. We also consider stability frames as -- . Finally, we conclude this note by raising a conjecture connecting frame theory and operator theory

math.FA↗

arXiv2022

Study on operator representation of frames in Hilbert spaces

The purpose of this paper is to give an overview of the operator structure of frames, where the operator belongs to certain classes of linear operators and the element belongs to $H$. We discuss the size of the set of such elements. Also, for a given frame and any, some results are obtained for . Finally, we conclude this note by raising several questions connecting frame theory and operator theory.

math.FA↗

arXiv2020

Lambert Multipliers Between $L^P$-spaces as a Banach Algebra

For 1 â‰¤ p < âˆž, it is known that the set K^*_p contains of all Lambert multipliers acting between L^p-spaces is a Banach space. In this study, we introduce a new induced norm by conditional expectation operators to show that K^*_p is a commutative Banach algebra with respect to this norm. Furthermore, in main result, the Fredholm *-multiplication operators on L^p-spaces are characterized, and some more results are obtained.

math.FA↗

arXiv2020

On R-duals of type III in Hilbert spaces

Following work by Casazza, Kutyniok and Lammers, and extensions by Stoeva and Christensen, we provide some novel characterizations of R-dual sequences of type III in Hilbert spaces. We systematically extend the construction procedure by basing it on a choice of an antiunitary involution. For certain classes of R-duals of type III, we derive a representation of the associated frame operator in terms of spectral measures.

math.RT↗

arXiv2019

Viewing *-multiplication operators between Orlics spaces

In this paper, Lambert multipliers acting between Orlicz spaces are characterized based on conditional expectation operators. Also, we give necessary and sufficient conditions to *-multiplication operators to be closed range. Finally, the necessary condition under which a *-multiplication operator to be Fredholm operator is investigated.

math.FA↗

arXiv2018

K-g-frames and approximate K-g-duals in Hilbert spaces

Approximate duality of frame pairs have been investigated by Christensen and Laugesen in (Sampl. Theory Signal Image Process., 9, 2011, 77-90), with the motivation to obtain an important applications in Gabor systems, wavelets and general frame theory. In this paper we obtain some of the known results in approximate duality of frames to K-g-frames. We also obtain new K-g-frames and approximate K-g-duals from a K-g-frame and an approximate K-g-dual. Finally, we give an equivalent condition under which the subsequence of a K-g-frame still to be a K-g-frame.

math.FA↗

arXiv2016

A classification of anisotropic Besov spaces

We study (homogeneous and inhomogeneous) anisotropic Besov spaces associated to expansive dilation matrices $A \in {\rm GL}(d,\mathbb{R})$, with the goal of clarifying when two such matrices induce the same scale of Besov spaces. For this purpose, we first establish that anisotropic Besov spaces have an alternative description as decomposition spaces. This result allows to relate properties of function spaces to combinatorial properties of the underlying coverings. This principle is applied to the question of classifying dilation matrices. It turns out the scales of homogeneous and inhomogeneous Besov spaces differ in the way they depend on the dilation matrix: Two matrices $A,B$ that induce the same scale of homogeneous Besov spaces also induce the same scale of inhomogeneous spaces, but the converse of this statement is generally false. Furthermore, the question whether $A,B$ induce the same scale of homogeneous spaces is closely related to the question whether they induce the same scale of Hardy spaces; the latter question had been previously studied by Bownik. We give a complete characterization of the different types of equivalence in terms of the Jordan normal forms of $A,B$.

math.FA↗