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On the Multidimensional Boundary Analogues of the Morera Theorem

In: Multidimensional Integral Representations

Author

Listed:
  • Alexander M. Kytmanov

    (Siberian Federal University, Institute of Mathematics and Computer Science)

  • Simona G. Myslivets

    (Siberian Federal University, Institute of Mathematics and Computer Science)

Abstract

This chapter contains some results related to the analytic continuation of functions given on the boundary of a bounded domain $$D \subset \mathbb{C}^{n}$$ , n > 1, to this domain. The subject is not new. Results about the continuation of the Hartogs–Bochner theorem are well known and have already became classical. They are the subject of many monographs and surveys (see, for example, Aizenberg and Yuzhakov, Khenkin, Rudin, and many others). Here we will discuss boundary multidimensional variants of the Morera theorem. We desire to show how integral representations can be applied to the study of analytic continuation of functions. The same question about continuation connected with the direction about gluing discs can also be applied to the above Morera theorems based on the theory of extremal discs, developed by Lempert. However, since it is based on other ideas and methods, it does not fit into our book devoted to integral representations and their applications.

Suggested Citation

  • Alexander M. Kytmanov & Simona G. Myslivets, 2015. "On the Multidimensional Boundary Analogues of the Morera Theorem," Springer Books, in: Multidimensional Integral Representations, edition 1, chapter 0, pages 75-117, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-21659-1_3
    DOI: 10.1007/978-3-319-21659-1_3
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