  Aims: To study the presence of superoscillations in coronal magnetoacoustic
waves and its possible role in heating coronal loops through the strong and
localized gradients they generate on the wave. Methods: An analytic model is
built for the transition between a sausage and a kink wave modes propagating
along field lines in the corona. We compute in this model the local
frequencies, the wave gradients and the associated heating rates due to
compressive viscosity. Results: We find superoscillations associated with the
transition between wave modes accompanying the wave dislocation that shifts
through the wave domain. Frequencies 10 times higher than the normal frequency
are found. This means that a typical 3-minute coronal wave will locally
oscillate in 10 to 20 seconds. Such high frequencies bring up strong gradients
that efficiently dissipate the wave through compressive viscosity. We compute
the associated heating rates. Locally, they are very strong, largely
compensating typical radiative losses.
  Conclusions: We find a new heating mechanism associated to magnetoacoustic
waves in the corona. Heating due to superoscillations only happens along
particular field lines with small cross sections, comparable in size to coronal
loops, inside the much larger magnetic flux tubes and wave propagation domain.
