A Note on the Alexander Theorem on the Complex Plane

@article{SylwesterZając2012,
abstract = {We investigate the Banach manifold consisting of complex $^r$ 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.},
author = {Sylwester Zając},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {Fredholm mapping; Fredholm index; operator},
language = {eng},
number = {3},
pages = {249-258},
title = {A Note on the Alexander Theorem on the Complex Plane},
url = {http://eudml.org/doc/281240},
volume = {60},
year = {2012},
}

TY - JOUR
AU - Sylwester Zając
TI - A Note on the Alexander Theorem on the Complex Plane
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2012
VL - 60
IS - 3
SP - 249
EP - 258
AB - We investigate the Banach manifold consisting of complex $^r$ 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.
LA - eng
KW - Fredholm mapping; Fredholm index; operator
UR - http://eudml.org/doc/281240
ER -