Functional Analysis and Its Applications

, Volume 50, Issue 2, pp 150–152 | Cite as

Generalized analytic functions, Moutard-type transforms, and holomorphic maps

  • P. G. GrinevichEmail author
  • R. G. Novikov


We continue the study of a Moutard-type transform for generalized analytic functions, which was initiated in [1]. In particular, we suggest an interpretation of generalized analytic functions as spinor fields and show that, in the framework of this approach, Moutard-type transforms for such functions commute with holomorphic changes of variables.

Key words

generalized analytic functions spinors Moutard transforms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. G. Grinevich and R. G. Novikov, J. Geom. Anal., DOI 10.1007/s12220–015-9657–8.Google Scholar
  2. [2]
    I. A. Taimanov, Teor. Mat. Phys., 182:2 (2015), 213–222; English transl.: Theor. Math. Phys., 182:2 (2015), 173–181.MathSciNetGoogle Scholar
  3. [3]
    I. A. Taimanov, Mat. Zametki, 97:1 (2015), 129–141; English transl.: Math. Notes, 97:1 (2015), 124–135.MathSciNetCrossRefGoogle Scholar
  4. [4]
    I. N. Vekua, Generalized Analytic Functions, Pergamon Press Ltd., 1962.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.L. D. Landau Institute for Theoretical PhysicsRussian Academy of SciencesChernogolovkaRussia
  2. 2.M. V. Lomonosov Moscow State UniversityMoscowRussia
  3. 3.Centre de Mathématiques Appliquées, École Polytechnique, France Institute of Earthquake Prediction Theory and Mathematical GeophysicsRussian Academy of SciencesMoscowRussia

Personalised recommendations