Holomorphic operator families on a manifold with edge

✍ Scribed by W. Rungrottheera…

• Book ID: 120953410
• Publisher: SP Birkhäuser Verlag Basel
• Year: 2013
• Tongue: English
• Weight: 289 KB
• Volume: 4
• Category: Article
• ISSN: 1662-9981
• DOI: 10.1007/s11868-013-0064-2

✦ Synopsis

We construct specific holomorphic families of operators on a manifold M with edge Y that have the order reducing property between weighted spaces H s,γ (M) for arbitrary weights γ varying in a prescribed compact interval and for all complex parameters in a strip parallel to the imaginary axis of arbitrary finite width. These operator functions are constructed as parameter-dependent elliptic elements of the edge calculus, here without additional conditions of trace and potential type. They play a role as operator-valued Mellin symbols in the higher corners pseudo-differential calculus.