Related papers: Reflectionless measures for Calder\'on-Zygmund Ope…

In this paper, we revisit the claim that many partition functions are invariant under reflecting temperatures to negative values (T-reflection). The goal of this paper is to demarcate which partition functions should be invariant under…

We prove a compact $T(1)$ theorem, involving quantitative estimates, analogous to the quantitative classical $T(1)$ theorem due to Stein. We also discuss the $C_c^\infty$-to-$CMO$ mapping properties of non-compact Calder\'on-Zygmund…

In this paper we develop a general theoretical tool for the establishment of the boundedness of notoriously difficult operators (such as potentials) on certain specific types of rearrangement-invariant function spaces from analogous…

In this paper we develop a kind of A_p theory for Calderon-Zygmund operators in a non-homogeneous setting. Let \mu be a Borel measure on \R^d which may be non doubling. The only condition that \mu must satisfy is \mu(B(x,r))\leq Cr^n for…

We study Schr\"odinger operators on $\R$ with measures as potentials. Choosing a suitable subset of measures we can work with a dynamical system consisting of measures. We then relate properties of this dynamical system with spectral…

In this expository article, we briefly survey the main known schemes of proof of sparse domination principles within harmonic analysis. We then use the one based on the Calder\'on-Zygmund decomposition to prove a dual sparse domination…

Second order equations of the form $z'' + A_0 z + D z'=0$ in an abstract Hilbert space are considered. Such equations are often used as a model for transverse motions of thin beams in the presence of damping. We derive various properties of…

While monotone operator theory is often studied on Hilbert spaces, many interesting problems in machine learning and optimization arise naturally in finite-dimensional vector spaces endowed with non-Euclidean norms, such as…

Let $T:[0,1]^d \rightarrow[0,1]^d$ be a piecewise expanding map with an absolutely continuous (with respect to the $d$-dimensional Lebesgue measure $m_d$) $T$-invariant probability measure $\mu$. Let $\left\{\mathbf{r}_n\right\}$ be a…

Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…

Given a bounded Lipschitz domain $D\subset \mathbb{R}^d$ and a Calder\'on-Zygmund operator $T$, we study the relations between smoothness properties of $\partial D$ and the boundedness of $T$ on the Zydmund space $\mathcal{C}_{\omega}(D)$…

We investigate the traceability of positive integral operators on $L^2(X,\mu)$ when $X$ is a Hausdorff locally compact second countable space and $\mu$ is a non-degenerate, $\sigma$-finite and locally finite Borel measure. This setting…

We show that a noninvasive,``negative-result measurement'' can be realized in quantum dot systems. The measurement process is studied by applying the Schr\"odinger equation to the whole system (including the detector). We demonstrate that…

The commutators of bilinear Calder\'on-Zygmund operators and point-wise multiplication with a symbol in $cmo$ are bilinear compact operators on product of Lebesgue spaces. This work shows that, for certain non-degenerate Calder\'on-Zygmund…

Suppose $L=-\Delta+V$ is a Schr\"odinger operator on $\mathbb{R}^n$ with a potential $V$ belonging to certain reverse H\"older class $RH_\sigma$ with $\sigma\geq n/2$. The main aim of this paper is to provide necessary and sufficient…

Topological measures and deficient topological measures generalize Borel measures and correspond to certain non-linear functionals. We study integration with respect to deficient topological measures on locally compact spaces. Such an…

For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing…

Chromatic effects are usually associated with refractive optics, so reflective telescopes are assumed to be free from them. We show that all-reflective optics still bears significant levels of such perturbations, which is especially…

Let $T$ be a multilinear Calder\'on-Zygmund operator of type $\omega$ with $\omega(t)$ being nondecreasing and satisfying a kind of Dini's type condition. Let $T_{\Pi\vec{b}}$ be the iterated commutators of $T$ with $BMO$ functions. The…

We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measure mu, and (ii) a definable group G in a simple theory such…