ON DETERMINING THE SPECTRUM OF PRIMORDIAL INHOMOGENEITY FROM THE COBE1 DMR SKY MAPS - METHOD

The natural approach to a spectral analysis of data distributed on the sky employs spherical harmonic decomposition. A common problem encoun tered in practical astronomy is the lack of full sky coverage in the a vailable data. For example, the removal of the Galactic plane data fro m the COBE DMR sky maps compromises Fourier analysis of the cosmic mic rowave background (CMB) temperature distribution due to the loss of or thogonality of the spherical harmonics. An explicit method for constru cting orthonormal functions on an incomplete (e.g., Galaxy-cut) sphere is presented. These functions should be used in the proper Fourier an alysis of the COBE DMR sky maps to provide the correct input for the d etermination of the spectrum of primordial inhomogeneity. The results of such an analysis are presented in an accompanying Letter. A similar algebraic construction of appropriate functions can be devised for ot her astronomical applications.