Related papers: An x-ray estimate in $R^n$

General Relativity in three or more dimensions can be obtained by taking the limit $\omega\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest…

Let $X$ be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $K^nX$ of $X$ in terms of the number of plane partitions. This computes the…

In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The…

We prove sharp $L^p-L^q$ estimates for averaging operators along general polynomial curves in two and three dimensions. These operators are translation-invariant, given by convolution with the so-called affine arclength measure of the curve…

Generalized quantum measurements with N distinct outcomes are used for determining the density matrix, of order d, of an ensemble of quantum systems. The resulting probabilities are represented by a point in an N-dimensional space. It is…

Using the local bijectivity of Keller maps, we give a proof of two-dimensional Jacobian conjecture.

The hydrogen atom is supposed to be described by a generalization of Schr\"{o}dinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions…

We develop a new approach to prove multiplier theorems in various geometric settings. The main idea is to use martingale transforms and a Gundy-Varopoulos representation for multipliers defined via a suitable extension procedure. Along the…

We prove a bilinear Kakeya inequality in the first Heisenberg group and a sharp bilinear Kakeya estimate for Euclidean curved tubes in $\R^2$. By adapting an argument of F\"assler, Pinamonti and Wald involving Heisenberg projections, we…

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

Why would anyone wish to generalize the already unappetizing subject of rigid body motion to an arbitrary number of dimensions? At first sight, the subject seems to be both repellent and superfluous. The author will try to argue that an…

We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem,…

We obtain an estimate for the volume of neighbourhoods of sets of large curvature in three-dimensional K\"ahler-Einstein manifolds.

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

We consider summations over digamma and polygamma functions, often with summands of the form (\pm 1)^n\psi(n+p/q)/n^r and (\pm 1)^n\psi^{(m)} (n+p/q)/n^r, where m, p, q, and r are positive integers. We develop novel general integral…

We survey progress on the Kakeya conjecture in Euclidean space, with an emphasis on developments that have occurred since the previous surveys by Wolff and Katz-Tao.

We calculate explicit estimates for the dimension of trajectories satisfying a certain growth bound. We generalize the classic results of Kurzweil by considering nonlinear nonautonomous and uniformly compact dynamical systems on normed…

We study large values of quadratic character sums with summation lengths exceeding the square root of the modulus. Assuming the Generalized Riemann Hypothesis, we obtain a new Omega result.

We improve previous results on dispersive decay for 1D Klein- Gordon equation. We develop a novel approach, which allows us to establish the decay in more strong norms and weaken the assumption on the potential.

Several identities similar to the Schlaefli formula are established for tetrahedra in a space of constant curvature.