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Session 17. Functional Analysis: relations to Complex Analysis and PDE
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Abel's functional equation and eigenvalues of composition operators on spaces of real analytic functions |
José Bonet, Universitat Politècnica de València,
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The talk is based on the joint work with P. Domański
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We present a full description of eigenvalues and eigenvectors of composition operators \(C_\varphi\) acting on the space \(A(R)\) of real analytic function on the real line \(R\)
for a real analytic self map \(\varphi\), as well as an isomorphic description of corresponding eigenspaces. We also completely characterize those self maps \(\varphi\) for which Abel's equation \(f\circ \varphi =f+1\) has a real analytic solution on the real line. Finally, we find cases when the operator \(C_\varphi\) has roots using a constructed embedding of \(\varphi\) into a so-called real analytic iteration semigroups.
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