From the 1 of 7 linked papers with an AI index.
7 papers
Sharp Ternary Martingale Isoperimetry and -adic Takagi-Type Lower Bounds
Natanael Alpay
The paper computes the exact isoperimetric profile for the ternary (3‑adic) martingale filtration on [0,1) and establishes sharp logarithmic lower bounds and endpoint L^α estimates…
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 (…
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 \…
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…
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…