Projection in a Space of Solenoidal Vector Fields期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Projection in a Space of Solenoidal Vector Fields

Authors:	M. I. Belishev A. K. Glasman

Abstract:	Let R³ be a bounded domain, $Omega ^xi : = { x in Omega \|{text{dist(}}x,partial Omega {text{) < }}xi } ,xi >0$ , a family of extending subdomains, and =(x) a positive function in $bar Omega ;let{text{ }}mathcal{H}: = { y = y(x)\|intlimits_Omega {dxvarepsilon left\| y right\|} ^2 < infty ,{text{ div }}varepsilon y = 0{text{ }}in{text{ }}Omega }$ be a space of -solenoidal vector fields, $mathcal{H}^xi : = { {text{y}} in mathcal{H}{text{\| suppy}} subset overline {Omega ^xi } } ,xi >0$ , a family of subspaces, G orthogonal projectors in onto $mathcal{H}^xi$ . A unitary transformation that diagonalizes the family of projectors {G} is constructed: it takes $int {xi dG^xi }$ to the operator of multiplication by the independent variable. The isometry of this transformation is proved with the help of the operator Riccati equation for the NeumanntoDirichlet mapping. Bibliography: 8 titles.

Keywords:
本文献已被 SpringerLink 等数据库收录！