Поступления иностранных книг в библиотеки ННЦ в 2003 г.
Институт математики |  |
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Lauter R. Pseudodifferential analysis on conformally compact spaces. - Providence, 2003. - XVI, 92 p. - (Memoirs of the Amer. math. soc., ISBN 0-8218-3272-7; N 777). - Псевдодифференциальный анализ на конформно компактных пространствах
Оглавление
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- The $0$-calculus on a manifold with boundary is a micro-localization of the Lie algebra of vector fields that vanish at the boundary. It has been used by Mazzeo, Melrose to study the Laplacian of a conformally compact metric. We give a complete characterization of those $0$-pseudodifferential operators that are Fredholm between appropriate weighted Sobolev spaces, and describe $C^{*}$-algebras that are generated by $0$-pseudodifferential operators. An important step is understanding the so-called reduced normal operator, or, almost equivalently, the infinite dimensional irreducible representations of $0$-pseudodifferential operators. Since the $0$-calculus itself is not closed under holomorphic functional calculus, we construct submultiplicative Fr?chet $*$-algebras that contain and share many properties with the $0$-calculus, and are stable under holomorphic functional calculus ($\Psi^{*}$-algebras in the sense of Gramsch). There are relations to elliptic boundary value problems.
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