Journal of Mathematical Sciences

, Volume 117, Issue 2, pp 3900–3909

On a Unitary Transform in the Space L2(Ω\ℝ3) Connected with the Weyl Decomposition

  • M. I. Belishev
Article

Abstract

In papers devoted to the dynamical inverse problem for the Naxwell system, in the context of the BC method, a unitary transform M: “solenoidal field → transversal field” was introduced. In this paper, M is complemented by a transform N: “potential field → longitudinal field.” Isometry and completeness of N are established. The transform U = MN mentioned in the title, turns out to be a unitary oprator. Bibliography: 5 titles.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    M. I. Belishev and A. K. Glasman, “Visualization of waves in the Maxwell dynamical system (the BC method),” Zap. Nauchn. Semin. POMI, 250, 49–61 (1998).Google Scholar
  2. 2.
    M. I. Belishev and A. K. Glasman, “On projection in the space of solenoidal vector fields,” Zap. Nauchn. Semin. POMI, 257, 16–43 (1999).Google Scholar
  3. 3.
    M. I. Belishev and A. K. Glasman, “The dynamical inverse problem for the Maxwell system:recovering the velocity in the regular zone (the BC method),” Algebra Analiz, 12, No. 2, 131–182 (2000).Google Scholar
  4. 4.
    E. B. Bykhovskii and N. V. Smirnov, “On orthogonal decompositions of the space of square integrable vector functions in a given domain,” Trudy MIAN, 59, 36–61 (1960).Google Scholar
  5. 5.
    O. A. Ladyzhenskaya, Mathematical Aspects of the Dynamics of a Viscous Incompressible Fluid [in Russian ], Nauka, Moscow (1970).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • M. I. Belishev
    • 1
  1. 1.St.Petersburg Department of theSteklov Mathematical InstituteRussia

Personalised recommendations