In this paper we study the dynamics of the stellar interior of the early red-giant star KIC 4448777 by asteroseismic inversion of 14 splittings of the dipole mixed modes obtained from Kepler observations .
In order to overcome the complexity of the oscillation pattern typical of red-giant stars , we present a procedure which involves a combination of different methods to extract the rotational splittings from the power spectrum .

We find not only that the core rotates faster than the surface , confirming previous inversion results generated for other red giants ( 31 ; 32 ) , but we also estimate the variation of the angular velocity within the helium core with a spatial resolution of \Delta r = 0.001 R and verify the hypothesis of a sharp discontinuity in the inner stellar rotation ( 32 ) .
The results show that the entire core rotates rigidly with an angular velocity of about \langle \Omega _ { c } / 2 \pi \rangle = 748 \pm 18 nHz and provide evidence for an angular velocity decrease through a region between the helium core and part of the hydrogen burning shell ; however we do not succeed to characterize the rotational slope , due to the intrinsic limits of the applied techniques .
The angular velocity , from the edge of the core and through the hydrogen burning shell , appears to decrease with increasing distance from the center , reaching an average value in the convective envelope of \langle \Omega _ { s } / 2 \pi \rangle = 68 \pm 22 nHz .
Hence , the core in KIC 4448777 is rotating from a minimum of 8 to a maximum of 17 times faster than the envelope .

We conclude that a set of data which includes only dipolar modes is sufficient to infer quite accurately the rotation of a red giant not only in the dense core but also , with a lower level of confidence , in part of the radiative region and in the convective envelope .