A Note on the Alexander Theorem on the Complex Plane

• Autorzy: Sylwester Zając
• Języki publikacji: EN

Abstrakty

EN

We investigate the Banach manifold consisting of complex $𝓒^r$ functions on the unit disc having boundary values in a given one-dimensional submanifold of the plane. We show that ∂/∂λ̅ restricted to that submanifold is a Fredholm mapping. Moreover, for any such function we obtain a relation between its homotopy class and the Fredholm index.

Kategorie tematyczne

• 32W05: ∂ ¯ and ∂ ¯ -Neumann operators
• 58B15: Fredholm structures

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: 60
• Numer: 3
• Strony: 249-258

Daty

wydano

2012

Twórcy

autor

Sylwester Zając

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/ba60-3-5