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We present a tomographic weak lensing analysis of the Kilo Degree Survey DataRelease 4 (KiDS-1000), using a new pseudo angular power spectrum estimator(pseudo-$C_{\ell}$) under development for the ESA Euclid mission. Over 21million galaxies with shape information are divided into five tomographicredshift bins, ranging from 0.1 to 1.2 in photometric redshift. We measuredpseudo-$C_{\ell}$ using eight bands in the multipole range $76<\ell<1500$ forauto- and cross-power spectra between the tomographic bins. A series of testswere carried out to check for systematic contamination from a variety ofobservational sources including stellar number density, variations in surveydepth, and point spread function properties. While some marginal correlationswith these systematic tracers were observed, there is no evidence of bias inthe cosmological inference. B-mode power spectra are consistent with zerosignal, with no significant residual contamination from E/B-mode leakage. Weperformed a Bayesian analysis of the pseudo-$C_{\ell}$ estimates by forwardmodelling the effects of the mask. Assuming a spatially flat $\Lambda$CDMcosmology, we constrained the structure growth parameter $S_8 =\sigma_8(\Omega_{\rm m}/0.3)^{1/2} = 0.754_{-0.029}^{+0.027}$. When combiningcosmic shear from KiDS-1000 with baryon acoustic oscillation and redshift spacedistortion data from recent Sloan Digital Sky Survey (SDSS) measurements ofluminous red galaxies, as well as the Lyman-$\alpha$ forest and itscross-correlation with quasars, we tightened these constraints to $S_8 =0.771^{+0.006}_{-0.032}$. These results are in very good agreement withprevious KiDS-1000 and SDSS analyses and confirm a $\sim 3\sigma$ tension withearly-Universe constraints from cosmic microwave background experiments.

KiDS & Euclid: Cosmological implications of a pseudo angular power spectrum analysis of KiDS-1000 cosmic shear tomography