Hopf bifurcation for functional equations |
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| Authors: | Jack K Hale JoséCarlos F de Oliveira |
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| Institution: | 1. Lefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University, Providence, Rhode Island 02912, USA;2. Instituto de Matematica e Estatistica, Universidade de São Paulo, São Paulo, Brasil 01451 |
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| Abstract: | Using a “concrete” representation for the adjoint, the spectrum of the class of linear transformations T which are bounded on Lp(?∞, ∞), 1 < p < ∞ into itself and which satisfy the functional equation Tt(a) = m(a) t(a), ?∞ < a < ∞, a ≠ 0, where m(a) = 1 or (sgn a) and where (t(a)f)(x) = f(ax), is studied. |
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