On the $\eta$-function for bisingular pseudodifferential operators

Autor:	Bohlen, Karsten
Rok vydání:	2015
Předmět:	Mathematics - Spectral Theory Primary 47G30 Secondary 46L80 46L85
Druh dokumentu:	Working Paper
Popis:	In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace property for the Wodzicki residue of bisingular operators and show how the residues of the $\eta$-function can be expressed in terms of the Wodzicki trace of a projection operator. Then we calculate the $K$-theory of the algebra of $0$-order (global) bisingular operators. With these preparations we establish the regularity properties of the $\eta$-function at the origin for global bisingular operators which are self-adjoint, elliptic and of positive orders. Comment: 20 pages, accepted Math. Nachrichten
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1506.04180 Zobrazit plný text záznamu View this record from Arxiv