  Subwavelength resonators are small scaled objects that exhibit contrasting
medium properties (eigher in intensity or sign) while compared to the ones of a
uniform background. Such contrasts allow them to resonate at specific
frequencies. There are two ways to mathematically define these resonances.
First, as the frequencies for which the related system of integral equations is
not injective. Second, as the frequencies for which the related resolvent
operator of the natural Hamiltonian has a pole. In this work, we consider, as
the subwavelength resonator, the Minneart bubble. We show that these two
mentioned definitions are equivalent. Most importantly,
  1. we derive the related resolvent estimates which are uniform in terms of
the size/contrast of the resonators. As a by product, we show that the
resolvent operators have no resonances in the upper half complex plane while
they exhibit two resonances in the lower half plane which converge to the real
axis, as the size of the bubble tends to zero. These resonances are related to
the Minnaert frequency (which constitutes their dominating real part).
  2. we derive the asymptotic estimates of the generated scattered fields which
are uniform in terms of the incident frequency and which are valid everywhere
in space (i.e. inside or outside the bubble).
  \end{enumerate} The dominating parts, for both the resolvent operator and the
scattered fields, are given by the ones of the point-scatterer supported at the
location of the bubble. In particular, these dominant parts are non trivial
(not the same as those of the background medium) if and only if the used
incident frequency identifies with the Minnaert one.
