A Note on the Alexander Theorem on the Complex Plane

• Autorzy: Zając S.

Identyfikatory

DOI

10.4064/ba60-3-5

• 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 ∂/∂λ− 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.

Słowa kluczowe

EN

Fredholm mapping; Fredholm index; delta operator

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2012
• Tom: Vol. 60, no 3
• Strony: 249--258
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Zając S.

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

Bibliografia

• [1] Y. Abramovich and C. Aliprantis, An Invitation to Operator Theory, Amer. Math. Soc., 2002.
• [2] H. Alexander, Gromov’s method and Bennequin’s problem, Invent. Math. 125 (1996), 135–148.
• [3] J. Milnor, Topology from the Differentiable Viewpoint, Princeton Univ. Press, 1997.
• [4] W. Rudin, Real and Complex Analysis, McGraw-Hill, 1974.
• [5] S. Smale, An infinite dimensional version of Sard’s theorem, Amer. J. Math. 87 (1965), 861–866.
• [6] I. Vekua, Generalized Analytic Functions, Pergamon Press, London, 1962.