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Applied and Computational Math Seminar

On feasibility of extrapolation of completely monotone functions.

Yury Grabovsky (Temple University)

Location:  Hill 005
Date & time: Wednesday, 20 March 2024 at 11:00AM - 12:00PM

In many areas of science and engineering people measure positive linear combinations of decaying exponentials and want to recover their parameters. The goal of this talk is to discuss feasibility of such a recovery. Positive linear combinations form a well-known class of completely monotone functions (CMFs). To quantify our question, we look for pairs of CMFs that have relative discrepancy (epsilon) on a given interval (a,b) as measured by the (L^2)-norm. Our goal is to estimate the largest relative discrepancy between them at a given point (x_0
ot in (a,b)). We show that this discrepancy can be made as large as one wishes, when (x_0 le a), and scales as (epsilon^{gamma(x_0)}), when (x_0 > b). An explicit formula for (gamma(x_0) in (0,1)) will be presented. This is a joint work with my graduate student Henry Brown and builds on a prior joint work with Narek Hovsepyan.

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