Open AccessOn relative widths of classes of multivariable functions that are defined as a convolution
Author(s) -
Leis Azar
Publication year - 1998
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/249801
Subject(s) - multivariable calculus , convolution (computer science) , mathematics , space (punctuation) , product (mathematics) , unit sphere , pure mathematics , order (exchange) , computer science , geometry , finance , control engineering , machine learning , artificial neural network , engineering , economics , operating system
We find exact order of estimate of relative widths in $L_1$ space of classes of periodic multivariable functions that are defined as a convolution of the product of one-dimensional kernels with functions from unit ball of $L_1$ space. By this we generalize known results on relative widths of classes of functions that are defined by bounds for $L_1$-norms of mixed derivatives.