Let P be the isotropic nearest neighbor transition operator on a homogeneous tree. We consider the λ-eigenfunctions of P for λ outside its l2 -spectrum spec(P ), i.e., the eigenfunctions with eigenvalue γ = λ − 1 of the Laplace operator Δ = P − I, and also the λ-polyharmonic functions, that is, the union n of the kernels of (Δ − γI) . We prove that, on a suitable Banach space generated by the λ-polyharmonic functions, the operator eΔ−γI is hypercyclic, although Δ − γI is not.

Universal properties of the isotropic Laplace operator on homogeneous trees

Joel M. Cohen;Mauro Pagliacci;
2022

Abstract

Let P be the isotropic nearest neighbor transition operator on a homogeneous tree. We consider the λ-eigenfunctions of P for λ outside its l2 -spectrum spec(P ), i.e., the eigenfunctions with eigenvalue γ = λ − 1 of the Laplace operator Δ = P − I, and also the λ-polyharmonic functions, that is, the union n of the kernels of (Δ − γI) . We prove that, on a suitable Banach space generated by the λ-polyharmonic functions, the operator eΔ−γI is hypercyclic, although Δ − γI is not.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/1532533
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