APPLIED MATH SEMINAR

Speaker: Kevin Luli, Mathematics, Yale University

Title:
C^{m,\omega} Extension by Bounded-depth Linear Operators

When/where: Tuesday, September 28th, 4:15 PM, AKW 200

Abstract:
In this talk, I will construct a particularly simple C^{m,\omega} (space of functions whose highest derivatives are \omega-continuous) extension operator for every
closed subset E of R^(n): The value of the extended function at every point in R^(n) is a linear
combination of the original function's values on a "predetermined," "bounded" subset S of
E. Here "predetermined" means independent of the given function on E and "bounded"
means having cardinality less than some constant determined solely by m (the smoothness)
and n (the dimension). Moreover, the m-th Taylor polynomial of the extended function at
x in R^(n) can be arbitrarily approximated by polynomials whose coefficients are determined
by a linear combination of the values of the original function on a predetermined, bounded
subset of E. In the absence of the \omega-continuity, it is not possible to construct such an operator.