4 papers
Representer Theorem in Complex Reproducing Kernel Hilbert Spaces with Applications to Fock and Hardy Spaces and Superoscillations
Natanael Alpay, Antonino De Martino, Kamal Diki
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (…
Polyanalytic Gaussian Radial Basis Function Kernel and Itô-Hermite Polynomials
Hendrik De Bie, Antonino De Martino, Kamal Diki
We introduce a polyanalytic extension of the Gaussian radial basis function (RBF) kernel by computing the action of the convolution operator on normalized Hermite functions. In par…
Superoscillations and the Klein-Gordon equation via the Fourier method
Kamal Diki, Simon Verbruggen
We investigate the time-evolution problem associated with the Klein-Gordon equation, using superoscillations as initial data. Additionally, the Segal-Bargmann transform is used to…
Towards Fock Spaces in Hypercomplex Analysis
Kamal Diki
The Bargmann-Fock space(or Fock space for short) is a fundamental example of reproducing kernel Hilbert spaces that has found fascinating applications across multiple fields of cur…