Related papers: The matrix $A_2$ conjecture fails, i.e. $3/2>1$

This paper completes the proof of the Ramanujan Conjecture for holomorphic Hilbert modular forms whose weights are all congruent modulo 2. As a consequence, the Weight-Monodromy Conjecture and the zeta function conjecture of Langlands are…

In any infinite dimensional Hilbert space H, a sequence P_n...P_1 x diverges in norm for some x \in H and orthogonal projections P_n \in {Q_1,..., Q_5}.

A large class of two-dimensional dilaton-gravity theories in asymptotically AdS$_2$ spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw-Teitelboim…

This paper is devoted to the $L^2$ norm error estimate of the Adini element for the biharmonic equation. Surprisingly, a lower bound is established which proves that the $ L^2$ norm convergence rate can not be higher than that in the energy…

We are interested in the norm of the inclusion between the standard weighted Bergman spaces $A^2_\alpha$ and $A^p_{\frac{p}{2} (\alpha + 2)-2}$, $p > 2$, which is conjectured to be contractive by O.F. Brevig, J. Ortega-Cerd\`a, K. Seip and…

Let $\mathcal{F}(\textbf{k},\mathfrak{q})$ be the set of primitive Hilbert modular forms of weight $\textbf{k}$ and prime level $\mathfrak{q}$, with trivial central character. We study the one-level density of low-lying zeros of $L(s,\pi)$…

Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The…

The wrapping transformation $W$ is a homomorphism from the semigroup of probability measures on the real line, with the convolution operation, to the semigroup of probability measures on the circle, with the multiplicative convolution…

Continuing a theme of Lerner and Hytonen-Perez, we establish an L^p(w) inequality for a Haar shift operator of bounded complexity, that quantifies the contribution of the A_infty characteristic of the weight to the L^p norm. Here,…

Here we show that Lerner's method of local mean oscillation gives a simple proof of the $A_2$ conjecture for spaces of homogeneous type: that is, the linear dependence on the $A_2$ norm for weighted $L^2$ Calderon-Zygmund operator…

Let $A, B$ be positive definite $n\times n$ matrices. We present several reverse Heinz type inequalities, in particular \begin{align*} \|AX+XB\|_2^2+ 2(\nu-1) \|AX-XB\|_2^2\leq \|A^{\nu}XB^{1-\nu}+A^{1-\nu}XB^{\nu}\|_2^2, \end{align*} where…

In this paper we discuss the notion of reducibility for matrix weights and introduce a real vector space $\mathcal C_\mathbb{R}$ which encodes all information about the reducibility of $W$. In particular a weight $W$ reduces if and only if…

We show that Lang's Flat Chain Conjecture (that is, without requiring finite mass of the underlying currents) fails for metric $k$-currents in $\mathbb{R}^d$ whenever $d\geq 2$ and $k\in\{1, \dots, d\}$. In all other cases, it holds. The…

In matrix analysis, the \textit{Wielandt-Mirsky conjecture} states that $$ dist(\sigma(A), \sigma(B)) \leq \|A-B\|, $$ for any normal matrices $ A, B \in \mathbb C^{n\times n}$ and any operator norm $\|\cdot \|$ on $C^{n\times n}$. Here…

We show that for any Hilbert space of distributions on $\textbf{R}^d$ which is translation and modulation invariant, is equal to $L^2(\textbf{R}^d)$, with the same norm apart from a multiplicative constant.

We prove that for a Calderon-Zygmund operator and weight w\in A_2, that it satisfies the linear in A2 bound due to Hytonen. Our proof will appeal to a distributional inequality used by several authors, adapted Haar functions, and standard…

Let $\mu_1$ be a complex number in the numerical range $W(A)$ of a normal matrix $A$. In the case when no eigenvalues of $A$ lie in the interior of $W(A)$, we identify the smallest convex region containing all possible complex numbers…

We prove a variant of the Arithmetic Fundamental Lemma conjecture of Wei Zhang for n=2. More precisely, we consider the deformation lengths of certain quasi-homomorphisms of quasi-canonical lifts in the sense of Gross. We prove the…

We prove a limited range, off-diagonal extrapolation theorem that generalizes a number of results in the theory of Rubio de Francia extrapolation, and use this to prove a limited range, multilinear extrapolation theorem. We give two…

In this paper, we prove that for $s\in(1,2)$ there exists no totally lower irregular finite positive Borel measure $\mu$ in $\R^2$ with\break $\mathcal H^s(\supp\mu)<+\infty$ such that $\|R\mu\|\ci{L^\infty(m_2)}<+\infty$, where…