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Bernstein Functions and the Dirichlet Problem
SIAM Journal on Mathematical Analysis, 1989For a nonconvex, symmetric quadrilateral, the nonparametric minimal surface arising from an associated Dirichlet problem can be described in terms of the Weierstrass representation and the stereographic projection of its Gauss map. The Bernstein function—which arises by truncation of the re-entrant corner by a concave arc and by requiring the normal ...
Alan R. Elcrat, Kirk E. Lancaster
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On the Generating Function for Bernstein Polynomials
AIP Conference Proceedings, 2010The aim of this paper is to give main properties of the generating function of the Bernstein polynomials. We prove recurrence relations and derivative formula for Bernstein polynomials. Furthermore, some new results are obtained by using this generating function of these polynomials.
Mehmet Açíkgöz +4 more
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A Bernstein type inequality for algebraic functions
Indiana University Mathematics Journal, 1997Let \(V\subset\mathbb{R}^n\) be an algebraic variety of pure dimension \(m\) \((1\leq m\leq n-1)\). The purpose of this paper is to prove a local Bernstein inequality for certain families of algebraic functions that estimates the growth of an algebraic function bounded on a measurable subset of \(V\) in a neighborhood of a regular point containing this
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The dual basis functions for the Bernstein polynomials
Advances in Computational Mathematics, 1998The Bernstein polynomials \(B^n_i\), \(i=0,1,\dots,n\) form a basis of the \((n+1)\)-dimensional real linear space \(P^n\) of all polynomials of maximal degree \(n\). The dual basis functions \(D^n_j\) with respect to the inner product of \(L^2[0,1]\) can be represented as linear combinations of the \(B^n_i\).
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BERNSTEIN-SATO POLYNOMIALS AND FUNCTIONAL EQUATIONS
Algebraic Approach to Differential Equations, 2010These notes are an expanded version of the lectures given in the frame of the I.C.T.P. School held at Alexandria in Egypt from 12 to 24 November 2007. Our purpose in this course was to give a survey of the various aspects, algebraic, analytic and formal, of the functional equations which are satisfied by the powers fs of a function f and involve a ...
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On localization of functions in the Bernstein space
Lithuanian Mathematical Journal, 2007For ϱ > 0, let $$L^1 (\mathbb{R})$$ be the closed subspace of L 1(ℝ) consisting of functions ƒ having the Fourier transforms ƒ concentrated in [−ϱ, ϱ]. Let a > 0. In this paper, we consider the problem of maximal localization of the L
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The Novel Stochastic Bernstein Method of Functional Approximation
First NASA/ESA Conference on Adaptive Hardware and Systems (AHS'06), 2006The stochastic Bernstein method (not to be confused with the Bernstein polynomials) is a novel and significantly improved non-polynomial global method of signal processing that is proving very useful for interpolating and for approximating data. It arose as an obvious extension of the work of Bernstein (it preserves some of the remarkable properties of
Kolibal, Joseph, Howard, Daniel
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Bernstein theorems for harmonic functions
1993Here and in the future we use the notation ...
Thomas Bagby, Norman Levenberg
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The weighted dual functionals for the univariate Bernstein basis
Applied Mathematics and Computation, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abedallah M. Rababah, Mohammad Al-Natour
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On exposed functions in Bernstein spaces
Lithuanian Mathematical Journal, 2008For σ > 0, the Bernstein space {ie427-01} consists of those L1(ℝ) functions whose Fourier transforms are supported by [−σ, σ]. Since {ie427-02} is separable and dual to some Banach space, the closed unit ball {ie427-03} of {ie427-04} has sufficiently large sets of both exposed and strongly exposed points: {ie427-05} coincides with the closed convex ...
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