Estimation of the integral modulus of smoothness of an even function of several variables with quasiconvex Fourier coefficients

1996 ◽  
Vol 3 (4) ◽  
pp. 379-400
Author(s):  
T. Tevzadze
Keyword(s):  
Fourier Coefficients ◽  
Modulus Of Smoothness ◽  
Integral Modulus ◽  
Several Variables ◽  
Function Of Several Variables

Estimation of the Integral Modulus of Smoothness of an Even Function of Several Variables with Quasiconvex Fourier Coefficients

1996 ◽  
Vol 3 (4) ◽  
pp. 379-400
Author(s):  
T. Tevzadze
Keyword(s):  
Fourier Coefficients ◽  
Modulus Of Smoothness ◽  
Integral Modulus ◽  
Several Variables ◽  
Function Of Several Variables

Abstract The estimate of the modulus of smoothness of an even function of several variables with quasiconvex Fourier coefficients obtained in this paper extends one result of S. A. Telyakovski.

On Estimating Integral Moduli of Continuity of Functions of Several Variables in Terms of Fourier Coefficients

1999 ◽  
Vol 6 (4) ◽  
pp. 307-322
Author(s):  
L. Gogoladze
Keyword(s):  
Fourier Coefficients ◽  
Moduli Of Continuity ◽  
Several Variables

Abstract Inequalities are derived which enable one to estimate integral moduli of continuity of functions of several variables in terms of Fourier coefficients.

On The Factorization of Partial Differential Equations

1987 ◽  
Vol 39 (4) ◽  
pp. 825-834 ◽  
Author(s):  
W. Dale Brownawell
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nevanlinna Theory ◽  
Algebraic Differential Equation ◽  
List Type ◽  
Variable Result ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Degenerate Cases

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.

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