Moutard transform approach to generalized analytic functions with contour poles

Piotr Grinevich (1) , Roman Novikov (2)

1 L.D. Landau Institute for Theoretical Physics of RAS
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We continue studies of Moutard-type transforms for the generalized analytic functions started in hal-01222481v1, hal-01234004v1. In particular, we show that generalized analytic functions with the simplest contour poles can be Moutard transformed to the regular ones, at least, locally. In addition, the later Moutard-type transforms are locally invertible.

Domaines: Equations aux dérivées partielles [math.AP]; Variables complexes [math.CV]; Analyse fonctionnelle [math.FA]

Piotr Grinevich, Roman Novikov. Moutard transform approach to generalized analytic functions with contour poles . Bulletin des Sciences Mathématiques, 2016, 140 (6), pp.638-656. ⟨hal-01249043⟩