The Moyal Product and Spectral Theory for a Class of Infinite Dimensional Matrices

Hansen Frank

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study tempered distributions that are multipliers of the Schwartz space relative to the Moyal product. They form an algebra N under the Moyal product containing the polynomials. The elements of N are represented as infinite dimensional matrices with certain growth properties of the entries. The representation transforms the Moyal product into matrix multiplication. Each real element of N allows a resolvent map with values in tempered distributions and an associated spectral resolution. This giaes a tool to study distributions associated with symmetric, but not necessarily self-adjoint operators.

Original languageEnglish
Pages (from-to)885-933
Number of pages49
JournalPublications of the Research Institute for Mathematical Sciences
Volume26
Issue number6
DOIs
Publication statusPublished - 1990

ASJC Scopus subject areas

  • Mathematics(all)

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