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On regularization in superreflexive Banach spaces by infimal convolution formulas

Manuel Cepedello-Boiso (1998)

Studia Mathematica

We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex C 1 , α functions converging to f uniformly on bounded sets and...

On Representations of Algebraic Polynomials by Superpositions of Plane Waves

Oskolkov, K. (2002)

Serdica Mathematical Journal

* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .

On semiregular families of triangulations and linear interpolation

Michal Křížek (1991)

Applications of Mathematics

We consider triangulations formed by triangular elements. For the standard linear interpolation operator π h we prove the interpolation order to be v - π h v 1 , p ≤ C h v 2 , p for p > 1 provided the corresponding family of triangulations is only semiregular. In such a case the well-known Zlámal’s condition upon the minimum angle need not be satisfied.

On some generalization of box splines

Zygmunt Wronicz (1999)

Annales Polonici Mathematici

We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.

On some properties of the Picard operators

Lucyna Rempulska, Karolina Tomczak (2009)

Archivum Mathematicum

We consider the Picard operators 𝒫 n and 𝒫 n ; r in exponential weighted spaces. We give some elementary and approximation properties of these operators.

On some quadrature rules with Laplace end corrections

Bogusław Bożek, Wiesław Solak, Zbigniew Szydełko (2012)

Open Mathematics

We investigate quadrature rules with Laplace end corrections that depend on a parameter β. Specific values of β yield sixth order rules. We apply our results to approximating the sum of slowly converging series s = Σi=1∞ f(i + 1/2) where f ∈ C 6 with its sixth derivative of constant sign on [m, ∞) and ∫ m∞ f(x)dx is known for m ∈ ℕ. Several examples show the efficiency of this method. This paper continues the results from [Solak W., Szydełko Z., Quadrature rules with Gregory-Laplace end corrections,...

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