Using Gabor analysis, we give a complete characterization of all lattice sampling and
interpolating sequences in the Fock space of polyanalytic functions, displaying a “Nyquist …

Why do solutions of linear analytic PDE suddenly break down? What is the source of these
mysterious singularities, and how do they propagate? Is there a mean value property for …

Harmonic functions are the solutions of the second-order partial differential equation∂ x ̲∂
x ̲ u= 0, where∂ x ̲ stands for the Dirac operator factorizing the Laplacian in R m. In this …

We continue the study initiated by HS Shapiro on Fischer decompositions of entire functions,
showing that such decomposition exist in a weak sense (we do not prove uniqueness) under …

∂ S= fm− 1 (s), s∈∂ S, where ν is the outward normal to the unit sphere∂ S. Numerous
papers deal with this problem. Of recent publications, we note [2, 3], where a representation …

Let ν ν be a rotation invariant Borel probability measure on the complex plane having
moments of all orders. Given a positive integer q, it is proved that the space of ν ν-square …

We consider non linear elliptic equations of the form $\Delta u= f (u,\nabla u) $ for suitable
analytic nonlinearity $ f $, in the vinicity of infinity in $\mathbb {R}^ d $, that is on the …

Dirichlet's Problem Let us start our story with the Dirichlet problem. This problem of finding a
harmonic function in a, say, smoothly bounded domain Ω⊂ Rn matching a given continuous …

Recurrence Relations for Orthogonal Polynomials and Algebraicity of Solutions of the
Dirichlet Problem Page 1 Recurrence Relations for Orthogonal Polynomials and …

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