Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 30, Tome 275 (2001), pp. 25-40
Citer cet article
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/
@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},
year = {2001},
volume = {275},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a2/}
}
TY - JOUR
AU - M. I. Belishev
TI - On a unitary transform in the space $L_2(\Omega,\mathbb R^3)$ connected with the Weyl decomposition
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2001
SP - 25
EP - 40
VL - 275
UR - http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a2/
LA - ru
ID - ZNSL_2001_275_a2
ER -
%0 Journal Article
%A M. I. Belishev
%T On a unitary transform in the space $L_2(\Omega,\mathbb R^3)$ connected with the Weyl decomposition
%J Zapiski Nauchnykh Seminarov POMI
%D 2001
%P 25-40
%V 275
%U http://geodesic.mathdoc.fr/item/ZNSL_2001_275_a2/
%G ru
%F ZNSL_2001_275_a2
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.
