2021/08/03 by Zorich, V. A.
#Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2108.01408
The global homeomorphism theorem for quasiconformal maps describes the following specifically higher-dimensional phenomenon: \em Locally invertible quasiconformal mapping f: \Rn → \Rn is globally invertible provided n > 2. We prove the following operator version of the global homeomorphism theorem. \em If the operator f: H → H acting in the Hilbert space H is locally invertible and is an operator of bounded distortion, then it is globally invertible.