The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Mihai Putinar -- Super-resolution of principal semi-algebraic sets
10h30-11h30
26 October 2022
Super-resolution of principal semi-algebraic sets
Abstract: A duality argument involving Lebesgue spaces associated to a background positive measure,
implies that among all shaded shapes, only those black and white, defined by a single inequality involving a prescribed space of test functions can be determined by finitely many generalized moments. As simple as it looks,
this non-constructive uniqueness statement is asking for an effective, possibly algorithmic, implementation. So far very little progress was made along these lines. From this point of view, the case of power moments and classical semi-algebraic sets in real Euclidean space stands aside, due to accumulated knowledge over several decades.The strong moment uniqueness of principal semi-algebraic sets, that is sub-level sets of a single real polynomial, carries a super-resolution phenomenon, in turn, derived from hard analysis estimates of oscillatory integrals. We will sketch the proof of the Holder norm continuity estimates of the inverse to the moment problem, in neighborhoods of black and white shapes determined by a single polynomial inequality. Low dimensional situations, essentially relying on Markov’s non-linear transform of moment sequences and a matrix model approach will serve as examples.
