Related papers: Chebyshev constants, transfinite diameter, and com…
We prove some trigonometric identities involving Chebyshev polynomials of second kind. The identities were inspired by atomic form factor calculations. Generalizations of these identities, if found, will help to increase the numerical…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
It is argued that the derivative expansion is a suitable method to deal with finite temperature field theory, if it is restricted to spatial derivatives only. Using this method, a simple and direct calculation is presented for the…
In this note we consider a question related to the high-dimensional generalization of the classical Severi's finiteness theorem for curves. We will introduce some background and then state the main result. The proof of the main result is…
Invertible compositions of one-dimensional maps are studied which are assumed to include maps with non-positive Schwarzian derivative and others whose sum of distortions is bounded. If the assumptions of the Koebe principle hold, we show…
Consider a rational family of planar rational curves in a certain region of interest. We are interested in finding an approximation to the implicit representation of the envelope. Since exact implicitization methods tend to be very costly,…
We study the variation of the convergence Newton polygon of a differential equation along a smooth Berkovich curve over a non-archimedean complete valued field of characteristic 0. Relying on work of the second author who investigated its…
Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.
We give Chebyshev-type quadrature formulas for certain new weight classes. These formulas are of highest possible degree when the number of nodes is a power of 2. We also describe the nodes in a constructive way, which is important for…
Generalized circumcenters have been recently introduced and employed to speed up classical projection-type methods for solving feasibility problems. In this note, circumcenters are enforced in a new setting; they are proven to provide…
The theory of classical types of curves in normed planes is not strongly developed. In particular, the knowledge on existing concepts of curvatures of planar curves is widespread and not systematized in the literature. Giving a…
The Chebyshev potential of a K\"ahler potential on a projective variety, introduced by Witt Nystr\"om, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus-invariant K\"ahler…
This paper aims to develop a theory of projective and affine structures on higher-dimensional varieties in positive characteristic. This theory deals with Frobenius-projective and Frobenius-affine structures, which have been previously…
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…
We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories…
Given a Fourier transformable measure in two dimensions, we find a formula for the intensity of its Fourier transform along circles. In particular, we obtain a formula for the diffraction measure along a circle in terms of the…
This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order {\alpha} . Expressions for the expansions of the evolution operators in powers of the…
For a compact convex set F in R^n, with the origin in its interior, we present a formula to compute the curvature at a fixed point on its boundary, in the direction of any tangent vector. This formula is equivalent to the existing ones, but…
Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but…
We prove global Sobolev regularity and pointwise upper bounds for the gradient of transition densities associated with second order differential operators in $\mathbb{R}^d$ with unbounded diffusion, drift and potential terms.