Hilbert bundles with ends

研究成果: ジャーナルへの寄稿学術誌査読

1 被引用数 (Scopus)

抄録

Given a countable metric space, we can consider its end. Then a basis of a Hilbert space indexed by the metric space defines an end of the Hilbert space, which is a new notion and different from an end as a metric space. Such an indexed basis also defines unitary operators of finite propagation, and these operators preserve an end of a Hilbert space. Then, we can define a Hilbert bundle with end, which lightens up new structures of Hilbert bundles. In a special case, we can define characteristic classes of Hilbert bundles with ends, which are new invariants of Hilbert bundles. We show Hilbert bundles with ends appear in natural contexts. First, we generalize the pushforward of a vector bundle along a finite covering to an infinite covering, which is a Hilbert bundle with end under a mild condition. Then we compute characteristic classes of some pushforwards along infinite coverings. Next, we will show the spectral decompositions of nice differential operators give rise to Hilbert bundles with ends, which elucidate new features of spectral decompositions. The spectral decompositions we will consider are the Fourier transform and the harmonic oscillators.

本文言語英語
ページ(範囲)291-322
ページ数32
ジャーナルJournal of Topology and Analysis
16
2
DOI
出版ステータス出版済み - 6月 1 2024

!!!All Science Journal Classification (ASJC) codes

  • 分析
  • 幾何学とトポロジー

フィンガープリント

「Hilbert bundles with ends」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル