We present a theory of quadratic time-frequency (TF) energy distributions that satisfy a covariance property and generalized marginal properties. The theory coincides with the characteristic function method of Cohen and Baraniuk in the special case of "conjugate operators."

2 Locally Stationary Processes 2 2.1 Time-varying spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Locally stationary processes depending on a parameter . . . . . . . . . . . . 7 2.3 Local Cosine Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Pseudo-di erential Covariance Operators . . . . . . . . . . . . . . . . . . . . 11 2.5 Time-Varying Fi...

Plemelj projection operators are introduced for spaces of square integrable functions defined over the boundaries of a class of compact real n-dimensional manifolds lying in C. These manifolds posses many properties similar to domains in R, and are consequently called domain manifolds. The key ingredients used here are techniques from both real and complex Clifford analysis. Analogues of the Ke...

The classical combinatorial relations between moments and cumulants of random variables are generalized into covariance-moment identities for stochastic integrals and divergence operators. This approach is based on cumulant operators defined by the Malliavin calculus in a general framework that includes Itô-Wiener and Poisson stochastic integrals as well as the Lie-Wiener path space. In particu...

Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza-Klein gauge fields and to the other side extrinsic curvature and torsion of embedded...

Building new and flexible classes of nonseparable spatio-temporal covariances and variograms has resulted a key point of research in the last years. The goal of this paper is to present an up-to-date overview of recent spatio-temporal covariance models taking into account the problem of spatial anisotropy. The resulting structures are proved to have certain interesting mathematical properties, ...