Journal of Mathematical Sciences

, Volume 166, Issue 1, pp 11–22

On a partially isometric transform of divergence-free vector fields


DOI: 10.1007/s10958-010-9840-1

Cite this article as:
Demchenko, M.N. J Math Sci (2010) 166: 11. doi:10.1007/s10958-010-9840-1

The paper deals with the so-called M-transform, which maps divergence-free vector fields in ΩT:= {x ∈ Ω| dist(x, ∂Ω) < T}, Ω ⊂⊂ \( \mathbb{R} \)3, to the space of transversal fields. The latter space consists of vector fields in ΩT tangential to the equidistant surfaces of the boundary ∂Ω. In papers devoted to the dynamical inverse problem for the Maxwell system, in the framework of the BC-method, the operator MT was defined for T < Tω, where Tω depends on the geometry of Ω. This paper provides a generalization for arbitrary T. It is proved that MT is partially isometric, and its intertwining properties are established. Bibliography: 6 titles.

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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