Related papers: Upper estimates of Christoffel function on convex …
We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…
We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our…
Estimates for invariant distances of convexifiable, $\C$-convexifiable and planar domains are given.
The purpose of this paper is twofold. First, we introduce the notion of a $\Gamma$-martingale on a Euclidean manifold with a boundary (i.e., the closure of an open connected domain in R d ), we provide its equivalent characterization…
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
We study the convolution function $$ C[f(x)] := \int_1^x f(y)f({x\over y}) {{\rm d} y\over y} $$ when $f(x)$ is a suitable number-theoretic error term. Asymptotics and upper bounds for $C[f(x)]$ are derived from mean square bounds for…
We show that the Christoffel function (CF) factorizes (or can be disintegrated) as the product of two Christoffel functions, one associated with the marginal and the another related to the conditional distribution, in the spirit of "the CF…
In this paper, new relations between the derivatives of the Legendre polynomials are obtained, and by these relations, new upper bounds for the Legendre coefficients of differentiable functions are presented. These upper bounds are sharp…
Performing both right and left multiplication operations using general regular matrix polynomials, which need not be monic and may possess leading coefficients of arbitrary rank, on a rectangular matrix of measures associated with mixed…
Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc…
We propose, theoretically investigate, and numerically validate an algorithm for the Monte Carlo solution of least-squares polynomial approximation problems in a collocation frame- work. Our method is motivated by generalized Polynomial…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Convolutional and differential distance estimation schemes are considered and, for…
Computing asymptotics of the recurrence coefficients of X1-Jacobi polynomials we investigate the limit of Christoffel function. We also study the relation between the normalized counting measure based on the zeros of the modified average…
In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
Upper bounds are derived for codes in Stiefel and Grassmann manifolds with given minimal chordal distance. They stem from upper bounds for codes in products of unit spheres and projective spaces. The new bounds are asymptotically better…
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced…
In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.
We give a new lower bound for the first gap $\lambda_2 - \lambda_1$ of the Dirichlet eigenvalues of the Schr{\"o}dinger operator on a bounded convex domain $\Omega$ in R$^n$ or S$^n$ and greatly sharpens the previous estimates. The new…