108 citations · 529 across the 96 of their papers we have counts for
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An approach to the Gaussian RBF kernels via Fock spaces
Daniel Alpay, Fabrizio Colombo, Kamal Diki +1
We use methods from the Fock space and Segal-Bargmann theories to prove several results on the Gaussian RBF kernel in complex analysis. The latter is one of the most used kernels i…
A Hörmander-Fock space
Daniel Alpay, Fabrizio Colombo, Kamal Diki +2
In a recent paper we used a basic decomposition property of polyanalytic functions of order in one complex variable to characterize solutions of the classical $\overline{\parti…
Hörmander's -method, -problem and polyanalytic function theory in one complex variable
Daniel Alpay, Fabrizio Colombo, Kamal Diki +2
In this paper we consider the classical -problem in the case of one complex variable both for analytic and polyanalytic data. We apply the decomposition property of…
Super-phenomena in arbitrary quantum observables
Andrew N. Jordan, Yakir Aharonov, Daniele C. Struppa +6
Superoscillations occur when a globally band-limited function locally oscillates faster than its highest Fourier coefficient. We generalize this effect to arbitrary quantum mechani…
Axially harmonic functions and the harmonic functional calculus on the S-spectrum
Fabrizio Colombo, Antonino De Martino, Stefano Pinton +1
The spectral theory on the S-spectrum was introduced to give an appropriate mathematical setting to quaternionic quantum mechanics, but it was soon realized that there were differe…
Discrete analytic functions, structured matrices and a new family of moment problems
Daniel Alpay, Fabrizio Colombo, Kamal Diki +2
Using Zeilberger generating function formula for the values of a discrete analytic function in a quadrant we make connections with the theory of structured reproducing kernel space…