Related papers: On semibounded Wiener-Hopf operators

Let $L=-\Delta+V$ be a Schr\"odinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this article, we will introduce weighted Hardy spaces $H^p_L(w)$…

We use integrals of left coideal subalgebras to develop Harmonic analysis for semisimple Hopf algebras. We show how $N^*,$ the space of functional on $N,$ is embedded in $H^*.$ We define a bilinear form on $N^*$ and show that irreducible…

We use the theory of abstract Wiener spaces to construct a probabilistic model for Berezin-Toeplitz quantization on a complete Hermitian complex manifold endowed with a positive line bundle. We associate to a function with compact support…

We define the total curvature of a semialgebraic embedding of a graph in the 3-dimensional Euclidean space. We prove that it satisfies a Chern-Lashof type inequality and we describe when the equality holds. We also prove a generalization of…

We consider a countably generated and uniformly closed algebra of bounded functions. We assume that there is a lower semicontinuous, with respect to the supremum norm, quadratic form and that normal contractions operate in a certain sense.…

We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…

Our goal is to compare various results for Toeplitz $T$ and Hankel $H$ operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define…

We consider a Schr\"odinger operator $H=-\Delta+V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. We prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized…

Let $H\subset\mathbb{Z}^d$ be a half-space lattice, defined either relative to a fixed coordinate (e.g.\ $H = \mathbb{Z}^{d-1}\!\times\!\mathbb{Z}_+$), or relative to a linear order $\preceq$ on $\mathbb{Z}^d$, i.e.\ $H = \{j\in\mathbb{Z}^d…

We prove a two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such…

It is proved that there does not exist any non zero function in $L^p(\R^n)$ with $1\leq p\leq 2n/\alpha$ if its Fourier transform is supported by a set of finite packing $\alpha$-measure where $0<\alpha<n$. It is shown that the assertion…

In this paper, we characterize all closed linear operators in a separable Hilbert space which are unitarily equivalent to an integral bi-Carleman operator in $L_2(R)$ with bounded and arbitrarily smooth kernel on $R^2$. In addition, we give…

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…

Considered are Wiener--Hopf plus Hankel operators $W(a)+H(b):L^p(\mathbb{R}^+)\to L^p(\mathbb{R}^+)$ with generating functions $a$ and $b$ from a subalgebra of $L^\infty(\mathbb{R})$ containing almost periodic functions and Fourier images…

Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…

Let (E,H,mu) be an abstract Wiener space and let D_V := VD, where D denotes the Malliavin derivative and V is a closed and densely defined operator from H into another Hilbert space G. Given a bounded operator B on G, coercive on the…

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy--Littlewood--Sobolev theorem in this context. In our main result, we investigate the dependence of…

Let $T$ be a bounded quaternionic normal operator on a right quaternionic Hilbert space $\mathcal{H}$. We show that $T$ can be factorized in a strongly irreducible sense, that is, for any $\delta >0$ there exist a compact operator $K$ with…

Let V be a finite dimensional real Euclidean Jordan algebra with the identity element 1. Let Q be the closed convex cone of squares. We show that the Wiener- Hopf compactification of Q is the interval (1-Q) \cap (-1+Q). As a consequence, we…

We give a new and very short proof of a theorem of Greiner asserting that a positive and contractive $C_0$-semigroup on an $L^p$-space is strongly convergent in case that it has a strictly positive fixed point and contains an integral…