scholarly journals Continuity modulus of stochastic homeomorphism flows for SDEs with non-Lipschitz coefficients

2006 ◽  
Vol 241 (2) ◽  
pp. 439-456 ◽  
Author(s):  
Jiagang Ren ◽  
Xicheng Zhang
Keyword(s):  
Continuity Modulus

Local continuity modulus for wiener and infinite dimensional OU processes

1994 ◽  
Vol 10 (2) ◽  
pp. 219-224 ◽  
Author(s):  
Lu Chuanrong ◽  
Shen Siwei ◽  
Wang Xiuyun
Keyword(s):  
Continuity Modulus ◽  
Infinite Dimensional

scholarly journals The least r-concave majorant of the continuity modulus ωr

2014 ◽  
Vol 30 (1) ◽  
pp. 117-122
Author(s):  
MARIA TALPAU DIMITRIU ◽  
◽  
Keyword(s):  
Modulus Of Continuity ◽  
Continuity Modulus

We define the least r-concave majorant for the modulus of continuity of order r on C[a, b], denoted by −r ω r and we establish the inequality ...

scholarly journals On Estimates for the Generalized Fourier-Dunkl Transform in the Space L2

MATEMATIKA ◽  
2018 ◽  
Vol 34 (1) ◽  
pp. 153-161
Author(s):  
Radouan Daher ◽  
Salah El Ouadih
Keyword(s):  
Dunkl Transform ◽  
Continuity Modulus ◽  
The Space L2

Two useful estimates are proved for the generalized Fourier-Dunkltransform in the space L2 on certain classes of functions characterized by thegeneralized continuity modulus.

scholarly journals Некоторые оценки для обобщенного преобразования Фурье, ассоциированного с оператором Чередника - Опдама

2018 ◽  
Author(s):  
H.S. Lafdal ◽  
R. Daher ◽  
El.O. Salah
Keyword(s):  
Fourier Transform ◽  
Translation Operator ◽  
Modulus Of Smoothness ◽  
Continuity Modulus ◽  
Generalized Translation Operator ◽  
Generalized Continuity ◽  
Generalized Translation ◽  
Translation Operators ◽  
Alpha Beta ◽  
Generalized Continuity Modulus

In the classical theory of approximation of functions on $\mathbb{R}^+$, the modulus of smoothness are basically built by means of the translation operators $f \to f(x+y)$. As the notion of translation operators was extended to various contexts (see [2] and [3]), many generalized modulus of smoothness have been discovered. Such generalized modulus of smoothness are often more convenient than the usual ones for the study of the connection between the smoothness properties of a function and the best approximations of this function in weight functional spaces (see [4] and [5]). In [1], Abilov et al. proved two useful estimates for the Fourier transform in the space of square integrable functions on certain classes of functions characterized by the generalized continuity modulus, using a translation operator. In this paper, we also discuss this subject. More specifically, we prove some estimates (similar to those proved in [1]) in certain classes of functions characterized by a generalized continuity modulus and connected with the generalized Fourier transform associated with the differential-difference operator $T^{(\alpha,\beta)}$ in $L^{2}_{\alpha,\beta}(\mathbb{R})$. For this purpose, we use a generalized translation operator.

On the Absolute Convergence of Fourier Series

1997 ◽  
Vol 4 (4) ◽  
pp. 333-340
Author(s):  
T. Karchava
Keyword(s):  
Fourier Series ◽  
Finite Number ◽  
Fourier Coefficients ◽  
Absolute Convergence ◽  
Sufficient Conditions ◽  
Trigonometric Fourier Series ◽  
Periodic Functions ◽  
Continuity Modulus ◽  
The Absolute ◽  
Necessary And Sufficient

Abstract The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2π-periodic functions which in [0, 2π] have a finite number of intervals of convexity, and whose 𝑛th Fourier coefficients are O(ω(1/𝑛; 𝑓)/𝑛), where ω(δ; 𝑓) is the continuity modulus of the function 𝑓.

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