Year: 2025
Type: article
Abstract: We establish higher-order trace formulas for pairs of contractions along a multiplicative path generated by a self-adjoint operator in a Schatten-von Neumann ideal, removing earlier stringent restrictions on the kernel and defect operator of the contractions and significantly enlarging the set of admissible functions. We also derive higher-order trace formulas for maximal dissipative operators under relaxed assumptions and new simplified trace formulas for unitary and resolvent comparable self-adjoint operators. The respective spectral shift measures are absolutely continuous and, in the case of contractions, the set of admissible functions for the n th-order trace formula on the unit circle includes the Besov class $B^n_{\infty , 1}(\mathbb {T})$ . Both aforementioned properties are new in the mentioned generality.
Source: Canadian Journal of Mathematics
Authors: Arup Chattopadhyay, Chandan Pradhan, Anna Skripka
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Award: G6062515657
OpenAlex ID: W4413382255