Abstract
The integral equation relating to the brightness distribution in a galaxy and in its image formed by an optical system characterized by a Gaussian (or a sum of Gaussians) point-spread function (PSF) is derived. Since the solution of this equation, attainable by any classical method, is numerically unstable, according to the ill-posed nature of the problem, an approximate and stable solution is obtainable by a first-order regularization in Tikhonov's sense. For the bright spike the application to M32 gives a radius of 2.1 arc sec a central surface brightness of 13.10 V mag arc sec−2 and a 12 V integrated magnitude.
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