The Moyal product and spectral theory for a class of infinite dimensional matrices (Q1174618)

Summary: 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 gives a tool to study distributions associated with symmetric, but not necessarily self-adjoint operators.