caa a22 4500 60552422X CHVBK 20210128100753.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10958-015-2309-5 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2309-5 Demchenko M. St. Petersburg Department of the V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia aut On Transforms of Divergence-Free and Curl-Free Fields, Associated with Inverse Problems [Elektronische Daten] [M. Demchenko] The M- and N-transforms acting, respectively, on divergence-free and curl-free vector fields on a Riemannian manifold with boundary are investigated. These transforms arise in studying the inverse problems of electrodynamics and elasticity theory. A divergence-free field is mapped by M to a field that is tangential to equidistants of the boundary. The N-transform maps a curl-free field to a field that is normal to equidistants. In preceding papers, the operators M and N were considered in the case of smooth equidistants, which is realized in a sufficiently small near-boundary layer. This allows one to consider transforms of fields supported in such a layer; it was proved that M and N are unitary in the corresponding spaces with L2-norms. In one of the papers, the case of fields on the whole manifold was considered, but almost all equidistants were assumed to be Lipschitz surfaces. It was proved that M is coisometric (i.e., the adjoint operator is isometric). In the present paper, the same result is obtained for both transforms in the general case with no constraints on equidistants at all. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/3(2015-04-01), 247-259 1072-3374 206:3<247 2015 206 10958 https://doi.org/10.1007/s10958-015-2309-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2309-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Demchenko M. St. Petersburg Department of the V. A. Steklov Institute of Mathematics of the Russian Academy of Sciences, St. Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/3(2015-04-01), 247-259 1072-3374 206:3<247 2015 206 10958