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Related papers: Sampling and interpolation in Bargmann-Fock spaces…

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We study multiple sampling and interpolation problems with unbounded multiplicities in the weighted Bergman space, both in the hilbertian case p = 2 and the uniform case p = +$\infty$.

Complex Variables · Mathematics 2022-02-16 Driss Aadi , Carlos Cruz , Andreas Hartmann , Karim Kellay

We study concentration operators acting on the Fourier symmetric Sobolev space $H$ consisting of functions $f$ such that $\int_{\mathbb{R}} |f(x)|^2(1+x^2) dx + \int_{\mathbb{R}} |\hat{f}(\xi)|^2(1+\xi^2) d\xi < \infty $. We find that the…

Classical Analysis and ODEs · Mathematics 2026-03-19 Denis Zelent

The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vall\'ee Poussin filters. These polynomials can be an useful device for many theoretical and…

Numerical Analysis · Mathematics 2020-08-04 Donatella Occorsio , Woula Themistoclakis

In this article, we consider a variation of the existence of Gabor frames in a probabilistic setting, in which we consider time-frequency shifts taken over random-periodic sets. We demonstrate that the method of selecting random-periodic…

Functional Analysis · Mathematics 2025-03-27 Sarthak Raj , S. Sivananthan

We refine a result of Matei and Meyer on stable sampling and stable interpolation for simple model sets. Our setting is model sets in locally compact abelian groups and Fourier analysis of unbounded complex Radon measures as developed by…

Functional Analysis · Mathematics 2024-09-05 Christoph Richard , Christoph Schumacher

This note, mostly expository, is devoted to Poincar{\'e} and log-Sobolev inequalities for a class of Boltzmann-Gibbs measures with singular interaction. Such measures allow to model one-dimensional particles with confinement and singular…

Probability · Mathematics 2020-09-02 Djalil Chafai , Joseph Lehec

By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1)…

Probability · Mathematics 2020-01-16 Vaios Laschos , Klaus Obermayer , Yun Shen , Wilhelm Stannat

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames $\mathcal{F} = \{f_i\}_{i \in I}$ and $\mathcal{E} =…

Functional Analysis · Mathematics 2007-05-23 R. Balan , P. G. Casazza , C. Heil , Z. Landau

We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…

Dynamical Systems · Mathematics 2024-12-23 Simon Baker , Osama Khalil , Tuomas Sahlsten

We investigate the structural properties of dual systems for nonstationary Gabor frames. In particular, we prove that some inverse nonstationary Gabor frame operators admit a Walnut-like representation, i.e. the operator acting on a…

Functional Analysis · Mathematics 2017-08-01 Nicki Holighaus

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show…

Differential Geometry · Mathematics 2011-11-24 Tapio Rajala

We obtain a refinement of the degrees of freedom estimate of Landau and Pollak. More precisely, we estimate, in terms of $\epsilon$, the increase in the degrees of freedom resulting upon allowing the functions to contain a certain…

Functional Analysis · Mathematics 2014-11-05 Luís Daniel Abreu , João M. Pereira

In this paper, we propose two methods for multivariate Hermite interpolation of manifold-valued functions. On the one hand, we approach the problem via computing suitable weighted Riemannian barycenters. To satisfy the conditions for…

Numerical Analysis · Mathematics 2022-12-15 Ralf Zimmermann , Ronny Bergmann

We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…

Statistics Theory · Mathematics 2025-10-28 Mara Daniels

The relationship between interpolation and separation properties of hypersurfaces in Bargmann-Fock spaces over $\mathbb{C} ^n$ is not well-understood except for $n=1$. We present four examples of smooth affine algebraic hypersurfaces that…

Complex Variables · Mathematics 2018-10-03 Vamsi Pingali , Dror Varolin

For the Weyl-Heisenberg group, convolutions between functions and operators were defined by Werner as a part of a framework called quantum harmonic analysis. We show how recent results by Feichtinger can be used to extend this definition to…

Functional Analysis · Mathematics 2024-10-11 Hans G. Feichtinger , Simon Halvdansson , Franz Luef

We consider sparseness properties of adaptive time-frequency representations obtained using nonstationary Gabor frames (NSGFs). NSGFs generalize classical Gabor frames by allowing for adaptivity in either time or frequency. It is known that…

Functional Analysis · Mathematics 2018-01-03 Emil Solsbæk Ottosen , Morten Nielsen

The properties of black-hole and neutron-star binaries are extracted from gravitational-wave signals using Bayesian inference. This involves evaluating a multi-dimensional posterior probability function with stochastic sampling. The…

General Relativity and Quantum Cosmology · Physics 2021-09-29 Virginia D'Emilio , Rhys Green , Vivien Raymond

In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.

Complex Variables · Mathematics 2017-09-05 Gerardo A. Chacon , Gerardo R. Chacon

We study the linear optical absorption of bulk semiconductors in the presence of a homogeneous constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption…

Mesoscale and Nanoscale Physics · Physics 2015-06-19 Federico Duque-Gomez , J. E. Sipe