Finite sums of ridge functions on convex subsets of R^n
Seminar
Speaker
Dr. A. Kuleshov, Moscow State University, Russia
Date
03/12/2018 - 15:10 - 14:00Add to Calendar
2018-12-03 14:00:00
2018-12-03 15:10:00
Finite sums of ridge functions on convex subsets of R^n
We prove that each function of one variable forming a continuous finite sum of ridge functions
on a convex body belongs to the VMO space on every compact interval of its domain. Also, we prove that for the existence of finite limits of the functions of one variable forming the sum at the
corresponding boundary points of their domains, it suffices to assume the Dini condition on the
modulus of continuity of some continuous sum of ridge functions on a convex body E at some boundary point. Further, we prove that the obtained (Dini) condition is sharp.
2nd floor Colloquium Room, Building 216
אוניברסיטת בר-אילן - Department of Mathematics
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Asia/Jerusalem
public
Place
2nd floor Colloquium Room, Building 216
Abstract
We prove that each function of one variable forming a continuous finite sum of ridge functions
on a convex body belongs to the VMO space on every compact interval of its domain. Also, we prove that for the existence of finite limits of the functions of one variable forming the sum at the
corresponding boundary points of their domains, it suffices to assume the Dini condition on the
modulus of continuity of some continuous sum of ridge functions on a convex body E at some boundary point. Further, we prove that the obtained (Dini) condition is sharp.
Last Updated Date : 03/12/2018
