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math.FA2026
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 (…
math.FA2026★ 1 cited
A new characterization of the Hardy space and of other spaces of analytic functions
Natanael Alpay
The Fock space can be characterized (up to a positive multiplicative factor) as the only Hilbert space of entire functions in which the adjoint of derivation is multiplication by t…
math.FA2025
Generalized Fock space and fractional derivatives with Applications to Uniqueness of Sampling and Interpolation Sets
Natanael Alpay, Paula Cerejeiras, Uwe Kähler
In this paper we introduce a Fock space related to derivatives of Gelfond-Leontiev type, a class of derivatives which includes many classic examples like fractional derivatives or…