This paper deals with the problem of estimating the correlogram of a stationary Gaussian process with known mean and variance. An unbiased estimate using random clipping by normally distributed random variable with non-zero mean is discussed, and the variance of the estimate is compared with those of competitors. Numerical comparison is performed for AR(2) process, and it indicates that the suggested estimate is preferable in many cases.
We study the spectral geometry of smooth maps of a compact Riemannian manifold in a Euclidean space, by using the notion of order (introduced by the first author). We give some best possible estimates of energy and total tension of a map in terms of order. Some applications to closed curves and harmonic maps are then obtained. In the last section, we relate the spectral geometry of the Gauss map of a submanifold to its topology and derive some topological obstructions to submanifolds to have a Gauss map of low type.
It is shown that if Q(z) is a non-constant polynomial, then all non-trivial solutions of y''+(ez+Q(z))y=0 have zeros with infinite exponent of convergence. Similar methods are used to settle a problem of M. Ozawa: if P(z) is a non-constant polynomial, all non-trivial solutions of y''+e−zy'+P(z)y=0 have infinite order.