Pointwise characterization of ideals of differentiable functions

1971 ◽  
Vol 13 (1-2) ◽  
pp. 143-168 ◽  
Author(s):  
Eugenio Filloy
Keyword(s):  
Differentiable Functions ◽  
Pointwise Characterization

Characterization of inverse-closed Beurling classes

1989 ◽  
Vol 105 (3) ◽  
pp. 495-501 ◽  
Author(s):  
Jamil A. Siddiqi ◽  
Mostefa Ider
Keyword(s):  
Constant Independent ◽  
Differentiable Functions ◽  
Infinitely Differentiable Functions ◽  
Image Position

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).

scholarly journals On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
J. M. Sepulcre
Keyword(s):  
Important Class ◽  
Exponential Polynomial ◽  
Critical Interval ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Polynomials ◽  
The Real ◽  
Linearly Independent ◽  
Pointwise Characterization

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.

scholarly journals On Whitney-type Characterization of Approximate Differentiability on Metric Measure Spaces

2014 ◽  
Vol 66 (4) ◽  
pp. 721-742 ◽  
Author(s):  
E. Durand-Cartagena ◽  
L. Ihnatsyeva ◽  
R. Korte ◽  
M. Szumańska
Keyword(s):  
Type Theorem ◽  
Maximal Functions ◽  
Metric Measure Spaces ◽  
Differentiable Structure ◽  
Differentiable Functions ◽  
Measure Spaces ◽  
Approximate Differentiability

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.

scholarly journals Pointwise characterization of the elastic properties of planar soft tissues: application to ascending thoracic aneurysms

2015 ◽  
Vol 14 (5) ◽  
pp. 967-978 ◽  
Author(s):  
Frances M. Davis ◽  
Yuanming Luo ◽  
Stéphane Avril ◽  
Ambroise Duprey ◽  
Jia Lu
Keyword(s):  
Elastic Properties ◽  
Soft Tissues ◽  
Thoracic Aneurysms ◽  
Pointwise Characterization

scholarly journals A criterion for normality of analytic mappings

2021 ◽  
pp. 1-9
Author(s):  
Marijan Marković
Keyword(s):  
Unit Ball ◽  
Unit Disk ◽  
Bloch Space ◽  
Type Theorem ◽  
Differentiable Functions ◽  
Analytic Mappings

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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