2 citations · 5 across the 11 of their papers we have counts for
12 papers
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…
Sharp Ternary Martingale Isoperimetry and -adic Takagi-Type Lower Bounds
Natanael Alpay
Let be the one-variation associated with the regular -adic martingale filtration on . We study the martingale isoperimetric profile \[ V_n(x):= \inf_{\substack{A\su…
Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces
Natanael Alpay, Emeric Battaglia
Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some…
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 (…
Fractional Supershifts and their associated Cauchy Evolution problems
Natanael Alpay
In this work, we extend the notion of supershifts and superoscillation sequence to fractional Fock spaces based on Gelfond-Leontiev fractional derivatives. We first introduce the f…
Sharp Lower Bounds for Dyadic Square Functions of indicator functions of sets
Natanael Alpay, Paata Ivanisvili
We study lower bounds for dyadic square functions of indicator functions. In the case of the dyadic square function we obtain a sharp lower bound: for every measurable $A \…
Thermal States on Mittag-Leffler Fock Space of the Slitted Plane
Natanael Alpay, Tiju Cherian John
Number states and thermal states form an important class of physical states in quantum theory. A mathematical framework for studying these states is that of a Fock space over an ap…
Varieties of unary-determined distributive -magmas and bunched implication algebras
Natanael Alpay, Peter Jipsen, Melissa Sugimoto
A distributive lattice-ordered magma (-magma) is a distributive lattice with a binary operation that preserves joins in both arguments, and w…
On the Mittag Leffler Bargmann (MLB) transform
Natanael Alpay, Kamal Diki
We introduce the Segal-Bargmann transform associated to the Mittag Leffler Fock space and study how it will be connected to the Fourier transform. We will discuss also the counterp…
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…