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Absolutely convergent Fourier series and generalized Lipschitz classes of functions

Ferenc Móricz (2008)

Colloquium Mathematicae

We investigate the order of magnitude of the modulus of continuity of a function f with absolutely convergent Fourier series. We give sufficient conditions in terms of the Fourier coefficients in order that f belong to one of the generalized Lipschitz classes Lip(α,L) and Lip(α,1/L), where 0 ≤ α ≤ 1 and L = L(x) is a positive, nondecreasing, slowly varying function such that L(x) → ∞ as x → ∞. For example, a 2π-periodic function f is said to belong to the class Lip(α,L) if | f ( x + h ) - f ( x ) | ≤ C h α L ( 1 / h ) for all x ∈ , h >...

An abstract version of Sierpiński's theorem and the algebra generated by A and CA functions

J. Cichoń, Michał Morayne (1993)

Fundamenta Mathematicae

We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass of the...

Analyse 2-microlocale et développementen série de chirps d'une fonction de Riemann et de ses généralisations

Daniel Boichu (1994)

Colloquium Mathematicae

En dimension 1 on analyse la fonction irrégulière r ( x ) = ∑ n = 1 ∞ n - p s i n ( n p x ) (p entier ≥ 2) en un point x 0 de dérivabilité (π est un tel point) et on démontre que le terme d’erreur est un chirp de classe (1 + 1/(2p-2), 1/(p-1), (p-1)/p). La fonction r(x) est dans l’espace 2-microlocal C x 0 s , s ' si et seulement si s+s’ ≤ 1 - 1/p et ps+s’≤ p - 1/2. En dimension 2, on obtient en (π,π) l’existence d’un plan tangent pour la surface z = ∑ m , n = 1 ∞ ( m 2 + n 2 ) - γ s i n ( m 2 x + n 2 y ) dès que γ>1.

Arrow-Hahn economic models with weakened conditions of continuity

Inese Bula, Dace Rika (2006)

Banach Center Publications

In this article we give descriptions of some economic models that are based on Arrow-Hahn economic model. Finally we consider a model with two major assumptions: first, there is discontinuous excess demand function and, second, if price goes to zero, then it is possible that excess demand may approach infinity. For this last new economic model the existence of quasi-equilibrium is proved.

Averages of quasi-continuous functions

Aleksander Maliszewski (1999)

Mathematica Bohemica

The goal of this paper is to characterize the family of averages of comparable (Darboux) quasi-continuous functions.

Currently displaying 21 – 40 of 242