[For the entire collection see Zbl 0572.00017.]
The problem of estimation of a trigonometric regression in the spatial series case is considered when observations are available on a piece of a realization of a stationary spatial point process. Consistency and asymptotic normality results are developed assuming that the spatial series and the point process are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient. A discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case is also given.