Related papers: Distorted Hankel integral operators

We investigate if, for a locally compact group $G$, the Fourier algebra $A(G)$ is biflat in the sense of quantized Banach homology. A central role in our investigation is played by the notion of an approximate indicator of a closed subgroup…

We investigate the commutativity and semi-commutativity of generalized singular integral operators of the form $P_{+} f P_{+} + P_{-} g P_{+} + P_{+} u P_{-} + P_{-} v P_{-}$ on $L^{2}$, where $P_{+}$ denotes the Riesz projection and…

In this paper, we discuss the boundedness of the fractional type Marcinkiewicz integral operators associated to surfaces, and extend a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type…

Let $T$ be a non-degenerate Calder\'on-Zygmund operator and let $b:\mathbb{R}^d\to\mathbb{C}$ be locally integrable. Let $1<p\leq q<\infty$ and let $\mu^p\in A_p$ and $\lambda^q\in A_q,$ where $A_{p}$ denotes the usual class of Muckenhoupt…

In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $\rho(x,t) = \rho_1(b x, b t)$ with $\rho_1(x,t)= (|x|^4 + t^2)^{1/4}$. We obtain $L^2$ boundedness properties using the…

Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in…

We study perturbed Bessel operators $L_{m^2}=- \partial^2_x + ( m^2 - \frac14 )\frac{1}{x^2} + Q(x)$ on $L^2]0,\infty[$, where $m\in\mathbb{C}$ and $Q$ is a complex locally integrable potential. Assuming that $Q$ is integrable near $\infty$…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

For fixed real numbers $c>0,$ $\alpha>-\frac{1}{2},$ the finite Hankel transform operator, denoted by $\mathcal{H}_c^{\alpha}$ is given by the integral operator defined on $L^2(0,1)$ with kernel $K_{\alpha}(x,y)= \sqrt{c xy}…

We introduce a family of differential-reflection operators $\Lambda_{A, \varepsilon}$ acting on smooth functions defined on $\mathbb R.$ Here $A$ is a Strum-Liouville function with additional hypotheses and $\varepsilon\in \mathbb R.$ For…

Let $\mathcal M$ be a factor von Neumann algebra with separable predual and let $T\in \mathcal M$. We call $T$ an irreducible operator (relative to $\mathcal M$) if $W^*(T)$ is an irreducible subfactor of $\mathcal M$, i.e., $W^*(T)'\cap…

We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…

Let $f$ and $g$ be analytic on the unit disc $\mathbb{D}$. The integral operator $T_g$ is defined by $ T_g f(z) = \int_0^z f(t)g'(t)\,dt$, $z \in \mathbb{D}$. The problem considered is characterizing those symbols $g$ for which $T_g$ acting…

Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also…

We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, the integral operator \begin{eqnarray*} S_{\varphi}F(z)=\int_{\mathbb{C}^n} F(w) e^{z…

We define a class of discrete operators that, in particular, include the delta and nabla fractional operators.

In this paper an analytic operator-valued generalized Feynman integral was studied on a very general Wiener space $C_{a,b}[0,T]$. The general Wiener space $C_{a,b}[0,T]$ is a function space which is induced by the generalized Brownian…

The Volterra-type integral operator plays an essential role in modern complex analysis and operator theory. Recently, Chalmoukis \cite{Cn} introduced a generalized integral operator, say $I_{g,a}$, defined by…

Let $x \in \mathbb{R}^d$, $d \geq 3,$ and $f: \mathbb{R}^d \rightarrow \mathbb{R}$ be a twice differentiable function with all second partial derivatives being continuous. For $1\leq i,j \leq d$, let $a_{ij} : \mathbb{R}^d \rightarrow…

We propose a nonlocal extension of the generalized Dirac oscillator (GDO) in $(1+1)$ dimensions by replacing the multiplicative interaction $f(x)$ with an integral operator $\hat F$ with kernel $f(x,x')$. The resulting Dirac equation…