Related papers: A comparison principle for convolution measures wi…
The Moore-Penrose algorithm provides a generalized notion of an inverse, applicable to degenerate matrices. In this paper, we introduce a covariant extension of the Moore-Penrose method that permits to deal with general relativity involving…
We establish generalized Gaussian bounds and local limit theorems with Gaussian-type error for the convolution powers of certain complex-valued functions on $\mathbb{Z}^d$. These global space-times estimates/error, which are sharp in…
We present two theorems describing analytic left-inverses of partial X-ray transforms. The first theorem concerns X-ray data collected with an arbitrary distribution of parallel projections; it contains a convolution-backprojection formula…
We prove that a local trilinear extension inequality on the paraboloid in three dimensions is equivalent to the Fourier restriction conjecture, and then we prove a variant involving smooth Alpert wavelets that represents the weakest such…
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
Uniform convergence of empirical norms - empirical measures of squared functions - is a topic which has received considerable attention in the literature on empirical processes. The results are relevant as empirical norms occur due to…
This article is concerned with a new method for the approximate evaluation of Fourier sine and cosine transforms. We develop and analyse a new quadrature rule for Fourier sine and cosine transforms involving transforming the integral to one…
The equivalence principle is treated on a mathematically rigorous base on sufficiently general subsets of a differentiable manifold. This is carried out using the basis of derivations of the tensor algebra over that manifold. Necessary…
A Fourier restriction estimate is obtained for a broad class of conic surfaces by adding a weight to the usual underlying measure. The new restriction estimate exhibits a certain affine-invariance and implies the sharp $L^p-L^q$ restriction…
This paper proposes a new theoretical perspective for studying the Hodge conjecture through an analytical framework based on constraint geometry. Our theory begins with a key observation: in compatible pair Spencer theory, a "differential…
In this paper we study the scale-space classification of signals via the maximal set of kernels. We use a geometric approach which arises naturally when we consider parameter variations in scale-space. We derive the Fourier transform…
In this paper, we consider the conormal bundle over a submanifold in a Finsler manifold and establish a volume comparison theorem. As an application, we derive a lower estimate for length of closed geodesics in a Finsler manifold. In the…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
We obtain new oscillation inequalities in metric spaces in terms of the Peetre $K-$functional and the isoperimetric profile. Applications provided include a detailed study of Fractional Sobolev inequalities and the Morrey-Sobolev embedding…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
In this paper, the concept of the classical $f$-divergence (for a pair of measures) is extended to the mixed $f$-divergence (for multiple pairs of measures). The mixed $f$-divergence provides a way to measure the difference between multiple…
We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure…
A general principle of non-equivalence for bodies and observers in different G potentials (GP) was derived from correspondence of the Einstein's equivalence principle either with optical physics or with gravitational experiments in which…