  We present the joint tomographic analysis of galaxy-galaxy lensing and galaxy
clustering in harmonic space, using galaxy catalogues from the first three
years of observations by the Dark Energy Survey (DES Y3). We utilise the
redMaGiC and MagLim catalogues as lens galaxies and the METACALIBRATION
catalogue as source galaxies. The measurements of angular power spectra are
performed using the pseudo-$C_\ell$ method, and our theoretical modelling
follows the fiducial analyses performed by DES Y3 in configuration space,
accounting for galaxy bias, intrinsic alignments, magnification bias, shear
magnification bias and photometric redshift uncertainties. We explore different
approaches for scale cuts based on non-linear galaxy bias and baryonic effects
contamination. Our fiducial covariance matrix is computed analytically,
accounting for mask geometry in the Gaussian term, and including non-Gaussian
contributions and super-sample covariance terms. To validate our harmonic space
pipelines and covariance matrix, we used a suite of 1800 log-normal
simulations. We also perform a series of stress tests to gauge the robustness
of our harmonic space analysis. In the $\Lambda$CDM model, the clustering
amplitude $S_8 =\sigma_8(\Omega_m/0.3)^{0.5}$ is constrained to $S_8 = 0.704\pm
0.029$ and $S_8 = 0.753\pm 0.024$ ($68\%$ C.L.) for the redMaGiC and MagLim
catalogues, respectively. For the $w$CDM, the dark energy equation of state is
constrained to $w = -1.28 \pm 0.29$ and $w = -1.26^{+0.34}_{-0.27}$, for
redMaGiC and MagLim catalogues, respectively. These results are compatible with
the corresponding DES Y3 results in configuration space and pave the way for
harmonic space analyses using the DES Y6 data.
