泛函分析

We investigate a random geometric graph model introduced by Bonato and Janssen. The vertices are the points of a countable dense set $S$ in a (necessarily separable) normed vector space $X$, and each pair of points are joined independently…

The purpose of this paper is to characterize several classes of functional identities involving inverses with related mappings from a unital Banach algebra $\mathcal{A}$ over the complex field into a unital $\mathcal{A}$-bimodule…

The pentablock, denoted as $\cP,$ is defined as follows: $$\cP= \left\{ (a_{21}, {\rm tr}(A), {\rm det}(A)) : A = [a_{ij}]_{2 \times 2} \text{ with } \|A\|<1 \right\}.$$ It originated from the work of Agler--Lykova--Young in connection with…

In the setting of the multidimensional Mellin analysis we introduce moduli of continuity and use them to define Besov-Mellin spaces. We prove that Besov-Mellin spaces are the interpolation spaces (in the sense of J.Peetre) between two…

We consider the shift operator $M_z$, defined on the Bloch space and the little Bloch space and we study the corresponding lattice of invariant subspaces. The index of a closed invariant subspace $E$ is defined as $\text{ind}(E) =…

Let $1<p<\infty$, let $H^p$ be the Hardy space on the unit circle, and let $H^p(w)$ be the Hardy space with a Muckenhoupt weight $w\in A_p$ on the unit circle. In 1988, B\"ottcher, Krupnik and Silbermann proved that the essential norm of…

Aluthge transform is a well-known mapping defined on bounded linear operators. Especially, the convergence property of its iteration has been studied by many authors. In this paper, we discuss the problem for the induced Aluthge transforms…

In this paper, we prove that every continuous $h$-mid-convex with suitable conditions on $h$ is $h$-convex function. Also, we extend Ostrowski theorem, Blumberg-Sierpinski theorem, Bernstein-Doetsch theorem, Mehdi theorem.

Let $ \mathbb{B}(\mathscr{H})$ represent the $C^*$-algebra, which consists of all bounded linear operators on $\mathscr{H},$ and let $N ( .) $ be a norm on $ \mathbb{B}(\mathscr{H})$. We define a norm $w_{(N,e)} (. , . )$ on $…

We show that the norm of the backward shift operator on $H^1$ is $2/\sqrt{3}$, and we identify the functions for which the norm is attained.

It is shown that the groups of finite energy (that is, Sobolev class $H^1$) paths and loops with values in a compact Lie group are amenable in the sense of Pierre de la Harpe, that is, every continuous action of such a group on a compact…

In this article, we prove the existence of a non-trivial hyperinvariant subspace for a subclass of compact perturbations of scalar multiple of a partial isometry. Later, we illustrate that this class contains several important classes of…

We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact abelian groups and Fourier analysis of unbounded complex Radon measures as developed by…

The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $\sigma$-compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled.…

We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined through a strongly recurrent self-similar local regular Dirichlet…

In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…

Fusion frames are widely studied for their applications in recovering signals from large data. These are proved to be very useful in many areas, such as, distributed processing, wireless sensor networks, packet encoding. Inspired by the…

We prove that the key property in models of Nonlinear Elasticity which corresponds to the non-interpenetration of matter, i.e. injectivity a.e., can be achieved in the class of weak limits of homeomorphisms under very minimal assumptions.…

In this work, we introduce the concept of direct integral of locally Hilbert spaces by using the notion of locally standard measure space (analogous to standard measure space defined in the classical setup), which we obtain by considering a…

We show that the volume of the boundary of a bounded Sobolev $(p,q)$-extension domain is zero when $1\leq q <p< \frac{qn}{(n-q)}.$