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We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
We study weighted transfer operators associated to a piecewise expanding map on a compact manifold, and a piecewise Holder weight, acting on Sobolev spaces. We bound the essential spectral radius in terms of a topological pressure for a…
Quaternionic analysis, which describes conformal maps from Riemann surfaces into $\mathbb{R}^3$ or $\mathbb{R}^4$, is extended to weakly conformal maps. As a consequence we present a new proof that on any compact Riemann surface $X$ the…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…
We prove exponential estimates for plurisubharmonic functions with respect to Monge-Ampere measures with Holder continuous potential. As an application, we obtain several stochastic properties for the equilibrium measures associated to…
The paper deals with the process of mathematical modeling representations of exponential and logarithmic functions hypercomplex number system of generalized quaternions via determining a linear differential equation with hypercomplex…
In a number of recent papers, the idea of generalized boundaries has found use in fractal and in multiresolution analysis; many of the papers having a focus on specific examples. Parallel with this new insight, and motivated by quantum…
The multiplicative Newton-like method developed by the author et al. is extended to the situation where the dynamics is restricted to the orthogonal group. A general framework is constructed without specifying the cost function. Though the…
A new kind of deformed calculus was introduced recently in studying of parabosonic coordinate representation. Based on this deformed calculus, a new deformation of Hermite polynomials is proposed, its some properties such as generating…
Fedorchuk's fully closed (continuous) maps and resolutions are applied in constructions of non-metrizable higher-dimensional analogues of Anderson, Choquet, and Cook's continua. Certain theorems on dimension-lowering maps are proved for…
An asymptotic framework is defined for the small parameter eta which quantifies a good separation between the extended bodies that make a weakly gravitating system. This is introduced within an alternative scalar theory of gravitation,…
This survey describes the recent advances in the construction of Markov partitions for nonuniformly hyperbolic systems. One important feature of this development comes from a finer theory of nonuniformly hyperbolic systems, which we also…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
Unlike the classical polynomial case there has not been invented up to very recently a tool similar to the Bernstein-Bezier representation which would allow us to control the behavior of the exponential polynomials. The exponential analog…
The kinematics of a robot manipulator are described in terms of the mapping connecting its joint space and the 6-dimensional Euclidean group of motions $SE(3)$. The associated Jacobian matrices map into its Lie algebra $\mathfrak{se}(3)$,…
A Nikishin-Maurey characterization is given for bounded subsets of weak-type Lebesgue spaces. New factorizations for linear and multilinear operators are shown to follow.
We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…