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Generalized Bernstein functions [PDF]
MATHEMATICA SCANDINAVICA, 2023 A class of functions called generalized Bernstein functions is studied. The fundamental properties of this class are given and its relation to generalized Stieltjes functions via the Laplace transform is investigated. The subclass of generalized Thorin-Bernstein functions is characterized in different ways.
Koumandos, Stamatis, Pedersen, Henrik L.
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2009
This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory.
Schilling, Rene +2 more
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This text is a self-contained and unified approach to Bernstein functions and their subclasses, bringing together old and establishing new connections. Applications of Bernstein functions in different fields of mathematics are given, with special attention to interpretations in probability theory.
Schilling, Rene +2 more
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Generating Functions for the $q$-Bernstein Bases
SIAM Journal on Discrete Mathematics, 2014We derive explicit formulas for the generating functions of the $q$-Bernstein basis functions in terms of $q$-exponential functions. Using these explicit formulas, we derive a collection of functional equations for these generating functions which we apply to prove a variety of identities, some old and some new, for the $q$-Bernstein bases.
Ron Goldman 0002 +2 more
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Approximation of Functions by a Bernstein-Type Operator
Canadian Mathematical Bulletin, 1972Various generalizations of the Bernstein operator, defined on C[0, 1] by the relation1.1wherehave been given. Note that bnk(x) is the well-known binomial distribution.
Pethe, S. P., Jain, G. C.
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Bernstein polynomials and dual functionals
Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, 2023The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.
Acu, Ana-Maria +2 more
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Bernstein functions, complete hyperexpansivity and subnormality-II
Integral Equations and Operator Theory, 2002The notion of subnormal operator was introduced in [Summa Brasil. Math. 2, 125--134 (1950; Zbl 0041.23201)] by \textit{P. R. Halmos}, while the notion of a completely hyperexpansive operator was introduced in [Proc. Am. Math. Soc. 124, 3745--3752 (1996; Zbl 0863.47017)] by \textit{A. Athavale}.
Athavale, Ameer, Ranjekar, Abhijit
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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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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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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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