85 citations · 203 across the 14 of their papers we have counts for
15 papers
PhaseJumps: fast computation of zeros from planar grid samples
Antti Haimi, Günther Koliander, José Luis Romero
We consider complex-valued functions on the complex plane and the task of computing their zeros from samples taken along a finite grid. We introduce PhaseJumps, an algorithm based…
Local repulsion between zeros and critical points of the Gaussian Entire Function
Antti Haimi, Lukas Odelius, José Luis Romero
We study the zeros and critical points of different indices of the standard Gaussian entire function on the complex plane (whose zero set is stationary). We provide asymptotics for…
Hyperuniformity and non-hyperuniformity of zeros of Gaussian Weyl-Heisenberg Functions
Naomi Feldheim, Antti Haimi, Günther Koliander +1
We study zero sets of twisted stationary Gaussian random functions on the complex plane, i.e., Gaussian random functions that are stochastically invariant under the action of the W…
Normality of smooth statistics for planar determinantal point processes
Antti Haimi, José Luis Romero
We consider smooth linear statistics of determinantal point processes on the complex plane, and their large scale asymptotics. We prove asymptotic normality in the finite variance…
Zeros of Gaussian Weyl-Heisenberg functions and hyperuniformity of charge
Antti Haimi, Günther Koliander, José Luis Romero
We study Gaussian random functions on the complex plane whose stochastics are invariant under the Weyl-Heisenberg group (twisted stationarity). The theory is modeled on translation…
Multiple sampling and interpolation in weighted Fock spaces of entire functions
Luis Alberto Escudero, Antti Haimi, José Luis Romero
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
Strict density inequalities for sampling and interpolation in weighted spaces of holomorphic functions
Karlheinz Gröchenig, Antti Haimi, Joaquim Ortega-Cerdà +1
Answering a question of Lindholm, we prove strict density inequalities for sampling and interpolation in Fock spaces of entire functions in several complex variables defined by a p…
Filtering with Wavelet Zeros and Gaussian Analytic Functions
Luis Daniel Abreu, Antti Haimi, Günther Koliander +1
We present the continuous wavelet transform (WT) of white Gaussian noise and establish a connection to the theory of Gaussian analytic functions. Based on this connection, we propo…
Contractive inequalities for Bergman spaces and multiplicative Hankel forms
Frédéric Bayart, Ole Fredrik Brevig, Antti Haimi +2
We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's i…
A Central Limit Theorem for Fluctuations in Polyanalytic Ginibre Ensembles
Antti Haimi, Aron Wennman
We study fluctuations of linear statistics in Polyanalytic Ginibre ensembles, a family of point processes describing planar free fermions in a uniform magnetic field at higher Land…
Density of Sampling and Interpolation in Reproducing Kernel Hilbert Spaces
Hartmut Führ, Karlheinz Gröchenig, Antti Haimi +2
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the spa…
Completeness of Gabor systems
Karlheinz Gröchenig, Antti Haimi, José Luis Romero
We investigate the completeness of Gabor systems with respect to several classes of window functions on rational lattices. Our main results show that the time-frequency shifts of e…
Bulk asymptotics for polyanalytic correlation kernels
Antti Haimi
We study reproducing kernels of weighted spaces of polyanalytic polynomials on the complex plane. The results include a universality result concerning local blow-ups of the kernels…
Asymptotic expansion of polyanalytic Bergman kernels
Haakan Hedenmalm, Antti Haimi
We consider mainly the Hilbert space of bianalytic functions on a given domain in the plane, square integrable with respect to a weight. We show how to obtain the asymptotic expans…
The polyanalytic Ginibre ensembles
Antti Haimi, Haakan Hedenmalm
We consider a polyanalytic generalization of the Ginibre ensemble. This models allowing higher Landau levels (the Ginibre ensemble corresponds to the lowest Landau level). We study…