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Joaquim Ortega-Cerda

Publications and source records attributed to Joaquim Ortega-Cerda.

5 recordsLinked to original sources
arXiv2008

The univalent Bloch-Landau constant, harmonic symmetry and conformal glueing

By modifying a domain first suggested by Ruth Goodman in 1935 and by exploiting the explicit solution by Fedorov of the Polyá-Chebotarev problem in the case of four symmetrically placed points, an improved upper bound for the univalent Bloch-Landau constant is obtained. The domain that leads to this improved bound takes the form of a disk from which some arcs are removed in such a way that the resulting simply connected domain is harmonically symmetric in each arc with respect to the origin. The existence of domains of this type is established, using techniques from conformal welding, and some general properties of harmonically symmetric arcs in this setting are established.

math.CV↗
arXiv2004

Interpolation and Sampling Hypersurfaces for the Bargmann-Fock space in higher dimensions

We study those smooth complex hypersurfaces W in C^n having the property that all holomorphic functions of finite weighted L^p norm on W extend to entire functions with finite weighted L^p norm. Such hypersurfaces are called interpolation hypersurfaces. We also examine the dual problem of finding all sampling hypersurfaces, i.e., smooth hypersurfaces W in C^n such that any entire function with finite weighted L^p norm is stably determined by its restriction to W. We provide sufficient geometric conditions on the hypersurface to be an interpolation and sampling hypersurface. The geometric conditions that imply the extension property and the restriction property are given in terms of some directional densities.

math.CV↗
arXiv2004

On Fourier frames

We solve the problem of Duffin and Schaeffer (1952) of characterizing those sequences of real frequencies which generate Fourier frames. Equivalently, we characterize the sampling sequences for the Paley-Wiener space. The key step is to connect the problem with de Branges' theory of Hilbert spaces of entire functions. We show that our description of sampling sequences permits us to obtain a classical inequality of H. Landau as a consequence of Pavlov's description of Riesz bases of complex exponentials and the John-Nirenberg theorem. Finally, we discuss how to transform our description into a working condition by relating it to an approximation problem for subharmonic functions. By this approach, we determine the critical growth rate of a nondecreasing function $ψ$ such that the sequence $\{\lamdda_k\}){k\in \Bbb Z}$ defined by $λ_k + ψ(λ_k)=k$ is a sampling.

math.CV↗
arXiv1999

Multipliers and weighted d-bar estimates

We study some size estimates for the solution of the equation d-bar u=f in one variable. The new ingredient is the use of holomorphic functions with precise growth restrictions in the construction of explicit solutions to the equation.

math.CV↗