scholarly journals Explicit computations with the divided symmetrization operator

2015 ◽  
Vol 144 (7) ◽  
pp. 2799-2810 ◽  
Author(s):  
Tewodros Amdeberhan
Keyword(s):  
Symmetrization Operator

scholarly journals Approximations of Symmetric Functions on Banach Spaces with Symmetric Bases

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2318
Author(s):  
Mariia Martsinkiv ◽  
Andriy Zagorodnyuk
Keyword(s):  
Analytic Functions ◽  
Symmetric Functions ◽  
Continuous Functions ◽  
Space Of Analytic Functions ◽  
Proper Subspace ◽  
Counter Example ◽  
Symmetric Bases ◽  
Symmetrization Operator ◽  
Uniformly Continuous ◽  
Positive Results

This paper is devoted to studying approximations of symmetric continuous functions by symmetric analytic functions on a Banach space X with a symmetric basis. We obtain some positive results for the case when X admits a separating polynomial using a symmetrization operator. However, even in this case, there is a counter-example because the symmetrization operator is well defined only on a narrow, proper subspace of the space of analytic functions on X. For X=c0, we introduce ε-slice G-analytic functions that have a behavior similar to G-analytic functions at points x∈c0 such that all coordinates of x are greater than ε, and we prove a theorem on approximations of uniformly continuous functions on c0 by ε-slice G-analytic functions.

Sign in / Sign up

Export Citation Format

Share Document