Gamma-ray light curves from statistically limited data; Hercules X-l

Summary  The problem of finding the light curve for noisy or sparse data is a familiar one. We develop a model-independent method which gives the light curve as a linear transformation of the data. Our approach emphasizes the fundamental choices between resolution and statistical error that is inherent in any data analysis. The analysis is treated as a special case of the general problem of data analysis based upon Fredholm equations of the first kind. The results, with certain approximations, are formally equivalent to the kernel density estimators but the interpretation is much different. We apply our technique to a TeV gamma-ray observation of the X-ray binary Hercules X-l.