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For symmetric α-stable processes, an analytic criterion for a measure being gaugeable was obtained by Z.-Q. Chen (2002), M. Takeda (2002) and M. Takeda and T. Uemura (2004). Applying it, we consider the ultra-contractivity of Feynman-Kac semigroups and expectations of the number of branches hitting closed sets in branching symmetric α-stable processes.

Gaugeability for Feynman-Kac functionals with applications to symmetric 𝛼-stable processes