2 citations · 5 across the 11 of their papers we have counts for
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Sharp discrete Hardy constants in low dimensions
Natanael Alpay
For , let denote the sharp constant in the nearest-neighbor Hardy inequality on with Euclidean inverse-square weight for functions vanishing at the origi…
The sharp discrete Hardy inequality on
Natanael Alpay
We determine the sharp constant in the nearest-neighbor Hardy inequality on with the Euclidean inverse-square weight. For every finitely supported function $u:\Z^3\to\C$, we…
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 (…
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…
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…