Homepage Link

On the Complex Representer Theorem and Relations between the Fock space and Superoscillations

Authora: Natanael Alpay, Kamal Dikim, and Antonino De Martino

Abstract

We introduce the complex counterpart for the representer theorem in machine learning. We discuss some learning and minimization problems in RKHS, where we look for the correct input data set to retrieve the kernel as a solution to the regression minimization problem. In particular, we retrieve the superoscillations in the Fock space, the RBF kernel in the RBF space, and the Blaschke factors in the Hardy space. Finally, we give an extension to other minimization problems via different loss functions. Joint work with Dr. Kamal Diki and Dr. Antonino De Martino .

Presetned at

  1. 2024 Advances in Operator Theory with Applications to Mathematical Physics:On the Complex Representer Theorem and Applications (Nov 19, 2024)