Geodesic
On a unitary transform in the space $L_2(\Omega,\mathbb R^3)$ connected with the Weyl decomposition
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 25-40

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In the papers devoted to the dynamical inverse problem for the Naxwell system, in the framework of the BC-method, a unitary transform $M$: "solenoidal field$\to$transversal field" was introduced. In this paper $M$ is complemented by a transform $N$: "potential field$\to$longitudinal field." Isometry and completeness of $N$ are established. The transform $U=M\oplus N$ mentioned in the title, turns out to be a unitary oprator. 
@article{ZNSL_2001_275_a2,
     author = {M. I. Belishev},
     title = {On a unitary transform in the space $L_2(\Omega,\mathbb R^3)$ connected with the {Weyl} decomposition},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {25--40},
     publisher = {mathdoc},
     volume = {275},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a2/}
}
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M. I. Belishev. On a unitary transform in the space $L_2(\Omega,\mathbb R^3)$ connected with the Weyl decomposition. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 25-40. http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a2/