English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We compute the $K$-groups of the $C^{*}$-algebra of bounded operatorsgenerated by the Boutet de Monvel operators with classical SG-symbols of order(0,0) and type 0 on $\mathbb{R}_{+}^{n}$, as defined by Schrohe, Kapanadze andSchulze. In order to adapt the techniques used in Melo, Nest, Schick andSchrohe's work on the K-theory of Boutet de Monvel's algebra on compactmanifolds, we regard the symbols as functions defined on the radialcompactifications of $\mathbb{R}_{+}^{n}\times\mathbb{R}^{n}$ and$\mathbb{R}^{n-1}\times\mathbb{R}^{n-1}$. This allows us to give usefuldescriptions of the kernel and the image of the continuous extension of theboundary principal symbol map, which defines a $C^{*}$-algebra homomorphism. Weare then able to compute the $K$-groups of the algebra using the standardK-theory six-term cyclic exact sequence associated to that homomorphism.

$K$-Theory of Boutet de Monvel algebras with classical SG-symbols on the half space