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By the method of classical potential theory, we obtain the integral representation of the two-parameter operator semigroup that describes the inhomogeneous Feller process on a closed interval [ , ] that is a result of pasting together two diffusion processes given on ( , ) and ( , ), respectively, where −∞ < < < < ∞.

Diffusions in one-dimensional bounded domains with reflection, absorption and jumps at the boundary and at some interior point