Related papers: Problems on spherical maximal functions

For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the…

This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for…

By using Jet Calculus as a consistent framework to describe multiparton dynamics we explain the peculiar evolution equation of fracture functions by means of the recently introduced extended fracture functions.

We undertake a general study of multifractal phenomena for functions. We show that the existence of several kinds of multifractal functions can be easily deduced from an abstract statement, leading to new results. This general approach does…

In this talk we show that any spherically symmetric spacetime admits locally a maximal spacelike slicing. The above condition is reduced to solve a decoupled system of first order quasi-linear partial differential equations. The solution…

Fluctuations in the return time statistics of a dynamical system can be described by a new spectrum of dimensions. Comparison with the usual multifractal analysis of measures is presented, and difference between the two corresponding sets…

In this paper, the spherical quasi-convexity of quadratic functions on spherically subdual convex sets is studied. Sufficient conditions for spherical quasi-convexity on spherically subdual convex sets are presented. A partial…

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…

We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…

We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…

For fixed natural numbers $r$ and $s$, where $2\leq s \leq r$, we consider a representation of numbers from the interval $[0;\frac{r}{s-1}]$ obtained by encoding numbers by means of the alphabet $A=\{0,1,...,r\}$ via the expansion…

The concept of splitting tessellations and splitting tessellation processes in spherical spaces of dimension $d\geq 2$ is introduced. Expectations, variances and covariances of spherical curvature measures induced by a splitting…

We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.

The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…

We survey the salient features and problems of conformal and superconformal mechanics and portray some of its developments over the past decade. Both classical and quantum issues of single- and multiparticle systems are covered.

This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…

We study Blaschke--Santal{\'o}-type inequalities for $N \ge 2$ sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{\'o}-type…

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic…

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.