On relative widths of classes of multivariable functions that are defined as a convolution | Zendy

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On 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.

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