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We present a proof of positivity of an invariant kernel, which is of basicimportance for the Staruszkiewicz theory of the quantum Coulomb field.Presented proof of positivity is independent of the Staruszkiewicz theory andis based on the classical Schoenberg's theorem for conditionally negativedefinite functions, as well as on the generalized Bochner's theorem.

Positivity of the Invariant Kernel Underlying Quantum Theory of the Coulomb Field