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math.FA2025
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…
math-ph2025
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…
math.CV2025
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…