On a Unitary Transform in the Space L2(Ω\ℝ3) Connected with the Weyl Decomposition
- M. I. Belishev
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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 = M ⊕ N mentioned in the title, turns out to be a unitary oprator. Bibliography: 5 titles.
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- M. I. Belishev and A. K. Glasman, “On projection in the space of solenoidal vector fields,” Zap. Nauchn. Semin. POMI, 257, 16–43 (1999).
- 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).
- 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).
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- On a Unitary Transform in the Space L2(Ω\ℝ3) Connected with the Weyl Decomposition
Journal of Mathematical Sciences
Volume 117, Issue 2 , pp 3900-3909
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- Kluwer Academic Publishers-Plenum Publishers
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- M. I. Belishev (1)
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- 1. St.Petersburg Department of the, Steklov Mathematical Institute, Russia