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Smooth approximation spaces based on a periodic system

Segeth, Karel (2015)

Programs and Algorithms of Numerical Mathematics

A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system exp ( - k x ) ....

Smoothing a polyhedral convex function via cumulant transformation and homogenization

Alberto Seeger (1997)

Annales Polonici Mathematici

Given a polyhedral convex function g: ℝⁿ → ℝ ∪ +∞, it is always possible to construct a family g ₜ t > 0 which converges pointwise to g and such that each gₜ: ℝⁿ → ℝ is convex and infinitely often differentiable. The construction of such a family g ₜ t > 0 involves the concept of cumulant transformation and a standard homogenization procedure.

Smoothness of the Green function for a special domain

Serkan Celik, Alexander Goncharov (2012)

Annales Polonici Mathematici

We consider a compact set K ⊂ ℝ in the form of the union of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions g ℂ ∖ K is estimated. Markov’s constants of the corresponding set are evaluated.

Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

Dryanov, Dimiter (2007)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.We characterize Paley-Wiener-Schwartz space of entire functions as a union of three-parametric linear normed subspaces determined by the type of the entire functions, their polynomial asymptotic on the real line, and the index p ≥ 1 of a Sobolev type Lp-summability on the real line with an appropriate weight function. An entire function belonging to a sub-space of the decomposition is exactly recovered by a sampling series, locally...

Sobre unos sistemas de números enteros algebraicos de D. S. Gorshkov y sus aplicaciones al cálculo.

Emiliano Aparicio Bernardo (1981)

Revista Matemática Hispanoamericana

El objeto del trabajo es la determinación de una cota superior del número real ρ definido comoρ = límn→∞ ρn ρn-n = MinPn∈Hn Max0≤x≤1 |Pn(X)|H n clase de polinomios no nulos con coeficientes en Z y grado menor o igual a n.En un artículo anterior (RMHA, 4 serie, t. XXXVIII, nº 6, 1978, pp. 259-270) el autor muestra que dado (λ1,...,λn) sistema completo de números reales algebraicos y algebraicamente conjugados, verificando:0 ≤ 1/λi+s ≤ 1 ∀i, ∃ s ∈ Zy definiendoδ = (∏i=1m |λi+s|)1/mse verifica ρ...

Solving a class of multivariate integration problems via Laplace techniques

Jean B. Lasserre, Eduardo S. Zeron (2001)

Applicationes Mathematicae

We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...

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