Results 171 to 180 of about 32,343 (193)

BERNSTEIN-SATO POLYNOMIALS AND FUNCTIONAL EQUATIONS

Algebraic Approach to Differential Equations, 2010
These 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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Bernstein theorems for harmonic functions

1993
Here and in the future we use the notation ...
Thomas Bagby, Norman Levenberg
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Bernstein estimator for unbounded density function

Journal of Nonparametric Statistics, 2007
Nonparametric estimation for an unknown probability density function f with a known compact support [0, 1] not necessarily bounded at x=0 is considered. For such class of density functions, we consider the Bernstein estimator. The uniform weak consistency and the uniform strong consistency on each compact I in (0, 1) are established for the Bernstein ...
T. Bouezmarni, J. M. Rolin
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Bernstein Functions and the Dirichlet Problem

SIAM Journal on Mathematical Analysis, 1989
For 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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A Bernstein type inequality for algebraic functions

Indiana University Mathematics Journal, 1997
Let \(V\subset\mathbb{R}^n\) 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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Saturation for Bernstein type rational functions

Acta Mathematica Hungarica, 1984
C. Balázs introduced the Bernstein type rational functions \[ R_ n(f,x)=(1/(1+a_ nx)^ n)\sum^{n}_{k=0}f(k/b_ n)\left( \begin{matrix} n\\ k\end{matrix} \right)(a_ nx)^ k\quad(x\geq 0) \] that can be used for the approximation of \(f\in C[0,\infty)\).
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On exposed functions in Bernstein spaces

Lithuanian Mathematical Journal, 2008
For 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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Bernstein copula characteristic function

Communications in Statistics - Theory and Methods, 2023
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Upper Bounds for Bernstein Basis Functions

2012
From Markov’s bounds for binomial coefficients (for which a short proof is given) upper bounds are derived for Bernstein basis functions of approximation operators and their maximum. Some related inequalities used in approximation theory and those for concentration functions are discussed.
Vijay Gupta, Tengiz Shervashidze
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Bernstein-Durrmeyer type operators preserving linear functions

2010
Many well-known approximating operators preserve linear functions. However, the operators introduced by the first author [Soochow J. Math. 23, No. 1, 115--118 (1997; Zbl 0869.41016)], as well as by the first author and \textit{P. Maheshwari} [Riv. Mat. Univ. Parma (7) 2, 9--21 (2003; Zbl 1050.41015)] do not preserve the test function \(e_1\).
Gupta, V., Duman, O.
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