Pointwise characterization of ideals of differentiable functions

1971 ◽  
Vol 13 (1-2) ◽  
pp. 143-168 ◽  
Author(s):  
Eugenio Filloy
1989 ◽  
Vol 105 (3) ◽  
pp. 495-501 ◽  
Author(s):  
Jamil A. Siddiqi ◽  
Mostefa Ider

In [1], J. Bruna studied the Beurling classes EM(I) of infinitely differentiable functions f defined on an interval I such that for every positive ε, there exists a constant Cε > 0 with the property thatwhere M = {Mn} is a given sequence of positive numbers. With the hypothesis that the class EM(ℝ) is differentiable, he proved that it is inverse-closed (in the sense that if fεEM(ℝ) and if f is bounded away from zero on ℝ, then its inverse f-1 lies in EM(ℝ)) if and only if the associated sequence A = {An = (Mn/n!)1/n} is almost increasing (i.e. Am ≤ KAn for all m ≤ n, where K > 0 is a constant independent of m and n).


2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. M. Sepulcre

We provide the proof of a practical pointwise characterization of the setRPdefined by the closure set of the real projections of the zeros of an exponential polynomialP(z)=∑j=1ncjewjzwith real frequencieswjlinearly independent over the rationals. As a consequence, we give a complete description of the setRPand prove its invariance with respect to the moduli of thecj′s, which allows us to determine exactly the gaps ofRPand the extremes of the critical interval ofP(z)by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.


2014 ◽  
Vol 66 (4) ◽  
pp. 721-742 ◽  
Author(s):  
E. Durand-Cartagena ◽  
L. Ihnatsyeva ◽  
R. Korte ◽  
M. Szumańska

AbstractWe study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, BV, and maximal functions.


2015 ◽  
Vol 14 (5) ◽  
pp. 967-978 ◽  
Author(s):  
Frances M. Davis ◽  
Yuanming Luo ◽  
Stéphane Avril ◽  
Ambroise Duprey ◽  
Jia Lu

Author(s):  
Marijan Marković

Abstract In this paper, we give a generalization and improvement of the Pavlović result on the characterization of continuously differentiable functions in the Bloch space on the unit ball in $\mathbb {R}^{m}$ . Then, we derive a Holland–Walsh type theorem for analytic normal mappings on the unit disk.


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