Abstract. It is well known that any (nontrivial) linear compact self-adjoint operator acting in a Hilbert space possesses at least one non-zero eigenvalue. We present a generalization of this to nonlinear mappings as in the title, and discuss the relations of our results with the Birkhoff-Kellogg Theorem on one side, and with the spectral properties of self-adjoint operators on the other.
Chiappinelli, R. (2007). Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkhoff-Kellogg theorem. In Discrete Contin. Dyn. Syst. 2007,Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference, suppl.ISBN: 978-1-60133-010-9; 1-60133-010-3 (pp.260-268). AIMS (American Institute of Mathematical Sciences).
Eigenvalues of homogeneous gradient mappings in Hilbert space and the Birkhoff-Kellogg theorem
CHIAPPINELLI, RAFFAELE
2007-01-01
Abstract
Abstract. It is well known that any (nontrivial) linear compact self-adjoint operator acting in a Hilbert space possesses at least one non-zero eigenvalue. We present a generalization of this to nonlinear mappings as in the title, and discuss the relations of our results with the Birkhoff-Kellogg Theorem on one side, and with the spectral properties of self-adjoint operators on the other.
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https://hdl.handle.net/11365/21628
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