The restrictions of functions holomorphic in a domain to curves lying on its boundary, and discrete $SL_2(R)$-spectraстатья
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Дата последнего поиска статьи во внешних источниках: 8 декабря 2019 г.
Аннотация:We consider the operator of restriction of functions holomorphic in a ball or a polydisc to curves lying on the Shilov boundary. It turns out that any function with polynomial growth near the boundary has such a restriction if the position of the curve satisfies a certain condition: if the domain is a ball, then the curve must be transversal to the standard contact distribution on the sphere, and if the domain is a polydisc, then the curve must be monotonic increasing with respect to all coordinates in the standard coordinatization of the torus. We use assertions of this kind to obtain a simple description of discrete inclusions in spectra (of minimal invariant subspaces) for several problems of $SL_2(\mathbb R)$-harmonic analysis.