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Let C[0,∞] be the space of continuous functions on the right half-axis R+ with finite limits at ∞, and let C[−∞,∞] be the space of continuous functions on the entire R that have finite limits at both −∞ and ∞. It has been known for some time that classical Feller–Wentzell boundary conditions for the Laplace operator in C[0,∞] are in one-to-one correspondence with certain subspaces of continuous functions on R that are invariant under the basic cosine family and the heat semigroup. In particular, the Robin boundary condition
f′(0)=γf(0),
where γ≥0 is a parameter, is linked with the subspace CγR⊂C[−∞,∞] of those f that satisfy f(−x)=f(x)−2γ∫x0e−γ(x−y)f(y)dy for x≥0. In this paper we find a natural operator Pγ that projects C[−∞,∞] onto CγR and with its help prove a surprising result saying that, for γ>0, CγR is complemented by the subspace CγF⊂C[−∞,∞] linked with the particular case of Feller–Wentzell boundary conditions describing slowly reflecting boundary (or sticky boundary), that is, with the condition
f”(0)=γf′(0).
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