FRB 180916 is a most intriguing source capable of producing repeating fast radio bursts with a periodic 16.3 day temporal pattern. The source is well positioned in a star forming region in the outskirts of a nearby galaxy at 150 Mpc distance. In this paper we report on the X-ray and γ-ray observations of FRB 180916 obtained by AGILE and Swift. We focused especially on the recurrent 5-day time intervals of enhanced radio bursting. In particular, we report on the results obtained in the time intervals Feb. 3 -8;Feb. 25; Mar. 5 -10; Mar. 22 -28, 2020 during a multiwavelength campaign involving high-energy and radio observations of FRB 180916. We also searched for temporal coincidences at millisecond timescales between the 32 known radio bursts of FRB 180916 and X-ray and MeV events detectable by AGILE. We do not detect any simultaneous event or any extended X-ray and γ-ray emission on timescales of hours/days/weeks.Our cumulative X-ray (0.3-10 keV) flux upper limit of 5 × 10 −14 erg cm −2 s −1 (obtained during 5-day active intervals from several 1-2 ks integrations) translates into an isotropic luminosity upper limit of L X,U L ∼ 1.5× 10 41 erg s −1 . Deep γ-ray observations above 100MeV over a many-year timescale provide an average luminosity upper limit one order of magnitude larger. These results provide the so-far most stringent upper limits on highenergy emission from the FRB 180916 source. Our results constrain the dissipation of
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