Related papers: Unboundedness Theorems for Symbols Adapted to Larg…

Let $\mathbb{H}$ be a $(d-1)$-dimensonal hyperbolic paraboloid in $\mathbb{R}^d$ and let $Ef$ be the Fourier extension operator associated to $\mathbb{H},$ with $f$ supported in $B^{d-1}(0,2)$. We prove that $\|Ef\|_{L^p (B(0,R))} \leq…

We use geometrical combinatorics arguments, including the ``hairbrush'' and x-ray arguments of Wolff and the sticky/plany/grainy analysis of Katz, Laba, and Tao, to show that Besicovitch sets in R^n have Minkowski dimension at least (n+2)/2…

We develop the theory of subproduct systems over the monoid $\mathbb{N}\times \mathbb{N}$, and the non-self-adjoint operator algebras associated with them. These are double sequences of Hilbert spaces $\{X(m,n)\}_{m,n=0}^\infty$ equipped…

We prove that for any given compact Riemannian manifold $N$ of dimension $n+1 \geq 3$ and any non-negative Lipschitz function $g$ on $N$, there exists a quasi-embedded, boundaryless hypersurface $M \subset N,$ of class $C^{2, \alpha}$ for…

Let $T$ be a $m$-linear Calder\'{o}n-Zygmund operator of type $\omega$ with $\omega$ being nondecreasing and $\omega \in$ Dini(1) and $[\vec{b},\,T]$ be the commutator generated by $T$ with symbols $\vec{b}=(b_1,\,\ldots,\,b_m)$ belonging…

We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $$u=\sum_{k=1}^\infty \langle u, y_k\rangle x_k,$$ then there exist nonzero scalars $\{\alpha_k\}_{k=1}^\infty$ such that…

Consider a $3$-uniform hypergraph of order $n$ with clique number $k$ such that the intersection of all its $k$-cliques is empty. Szemer\'edi and Petruska proved $n\leq 8m^2+3m$, for fixed $m=n-k$, and they conjectured the sharp bound…

A longstanding question in superstring/$M$ theory is does it predict supersymmetry below the string scale? We formulate and discuss a necessary condition for this to be true; this is the mathematical conjecture that all stable, compact…

We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold. Starting from an off-shell N = 2 superfield formalism, we…

Multivariate versions of the Kronecker theorem in the continuous multivariate setting has recently been published. These theorems characterize the symbols that give rise to finite rank multidimensional Hankel and Toeplitz type operators…

We show that for any $1<p<\infty$, the space $Hank_p(\mathbb{R}_+)\subseteq B(L^p(\mathbb{R}_+))$ of all Hankel operators on $L^p(\mathbb{R}_+)$ is equal to the $w^*$-closure of the linear span of the operators $\theta_u\colon…

Given an alphabet size $m\in\mathbb{N}$ thought of as a constant, and $\vec{k} = (k_1,\ldots,k_m)$ whose entries sum of up $n$, the $\vec{k}$-multi-slice is the set of vectors $x\in [m]^n$ in which each symbol $i\in [m]$ appears precisely…

We give a Riemannian structure to the set $\Sigma$ of positive invertible unitized Hilbert-Schmidt operators, by means of the trace inner product. This metric makes of $\Sigma$ a nonpositively curved, simply connected and metrically…

In 1887, Minkowski determined the least common multiple of the orders of all finite subgroups of $GL_n(\mathbb{Q})$; we refer to this number as $M(n)$. In (Katznelson, 1994), Katznelson provides the asymptotic behaviour of $M(n)$, with a…

Haas' theorem describes all partchworkings of a given non-singular plane tropical curve $C$ giving rise to a maximal real algebraic curve. The space of such patchworkings is naturally a linear subspace $W_C$ of the…

In this paper, first we prove that all finite dimensional special Heisenberg Lie superalgebras with even center have same dimension, say $(2m+1\mid n)$ for some non-negative integers $m,n$ and are isomorphism with them. Further, for a…

In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…

Benjamini, Finucane and the first author have shown that if (G_n,S_n) is a sequence of Cayley graphs such that |S_n^n|=O(n^D|S_n|), then the sequence (G_n,d_{S_n}/n) is relatively compact for the Gromov-Hausdorff topology and every cluster…

Let $\pi'$ be a fixed unitary cuspidal representation of $\mathrm{GL}(n)/\mathbb{Q}.$ We establish a subconvex bound in the $t$-aspect $$ L(1/2+it,\pi\times\pi')\ll_{\pi,\pi',\varepsilon}(1+|t|)^{\frac{n(n+1)}{4}-\frac{1}{4\cdot…

In this paper, we obtain analytical solution of an unsolved integral $\textbf{R}_{C}(m,n)$ of Srinivasa Ramanujan [$\textit{Mess. Math}$., XLIV, 75-86, 1915], using hypergeometric approach, Mellin transforms, Infinite Fourier cosine…