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Obtaining constraints from the largest scales of a galaxy survey ischallenging due to the survey mask allowing only partial measurement of largeangular modes. This scatters information from the harmonic-space 2-pointfunction away from the diagonal and introduces coupling between modes. In thispaper, we derive a custom eigenbasis adapted to any particular survey geometryso that all information is retained on the diagonal. At the expense of asomewhat complex pixel- and selection-function-window, the result is a diagonal2-point function with a simple shot noise, and a diagonal covariance matrix inthe case of a Gaussian random field. We derive the basis on the surface of asphere, and we use it to construct a 3D spherical Fourier-Bessel power spectrumestimator assuming a survey geometry that is separable in the angular andradial directions.

Harmonic analysis of isotropic fields on the sphere with arbitrary masks