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Keywords:
harmonic space; harmonic morphism; biharmonic space; biharmonic function; biharmonic morphism
harmonic space; harmonic morphism; biharmonic space; biharmonic function; biharmonic morphism
Summary:
Let $(X, \Cal H)$ and $(X',\Cal H')$ be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from $(X,\Cal H)$ to $(X',\Cal H')$ is a continuous map from $X$ to $X'$ which preserves the biharmonic structures of $X$ and $X'$. In the present work we study this notion and characterize in some cases the biharmonic morphisms between $X$ and $X'$ in terms of harmonic morphisms between the harmonic spaces associated with $(X,\Cal H)$ and $(X',\Cal H')$ and the coupling kernels of them.
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