Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere

Fourier-laplace Transform of Irreducible Regular Differential Systems on the Riemann Sphere

We show that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, when one only considers the part at finite distance, a polarizable regular twistor D-module. The associated holomorphic bundle out of the origin is therefore equipped with a natural harmonic metric with a tame behaviour near the origin.

Fourier–laplace Transform of Irreducible Regular Differential Systems on the Riemann Sphere, Ii

This article is devoted to the complete proof of the main theorem in the author’s paper of 2004 showing that the Fourier–Laplace transform of an irreducible regular differential system on the Riemann sphere underlies, at finite distance, a polarizable regular twistor Dmodule. 2000 Math. Subj. Class. Primary: 32S40; Secondary: 14C30, 34Mxx.

Erratum to “fourier-laplace Transform of Irreducible Regular Differential Systems on the Riemann Sphere”

This erratum corrects two mistakes in the proof of the main theorem of [7]. There are two mistakes in the proof of Theorem 1 in [7]: (i) In §3.1, point 5, we assert: “By simple homogeneity considerations with respect to τ , it suffices to prove the property in the neighbourhood of τ = 0.” It happens that homogeneity does not lead to such a statement. One has to prove the twistor property for th...

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere ∗

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomor-phic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over-and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion for...

On the Laplace transform decomposition algorithm for solving nonlinear differential equations