Finite-dimensional approximations of push-forwards on locally analytic functionals and truncation of least-squares polynomials

arXiv:2404.10769v1 Announce Type: cross
Abstract: This paper introduces a theoretical framework for investigating analytic maps from finite discrete data, elucidating mathematical machinery underlying the polynomial approximation with least-squares in multivariate situations. Our approach is to consider the push-forward on the space of locally analytic functionals, instead of directly handling the analytic map itself. We establish a methodology enabling appropriate finite-dimensional approximation of the push-forward from finite discrete data, through the theory of the Fourier--Borel transform and the Fock space. Moreover, …

abstract approximation arxiv cs.lg cs.na data framework least maps math.ds math.fa math.na multivariate paper polynomial space squares type