Characteristic Functionals

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Some Results on Bessel Functionals for GSp ( 4 )

We prove that every irreducible, admissible representation π of GSp(4, F ), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided π is not onedimensional. If π is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by π, and prove that Bessel functionals of a fixed type are unique. If π is supercuspidal, we do the...

Efficient Processing of Minkowski Functionals on a 3D Binary Image Using Binary Decision Diagrams

The Morphological Image Analysis characterizes binary digitized 3D images in terms of shape (geometry) and connectivity (topology) by means of the Minkowski functionals known from integral geometry. In three dimensions, these functionals correspond to the enclosed volume, surface area, mean breadth and connectivity (Euler characteristic). To compute these functionals, it is necessary to count t...

Equivalence of K-functionals and modulus of smoothness for fourier transform

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

A description of competing fusion systems q

A mathematical description of fusion is presented using category theory. A category of fusion rules is developed. The category definition is derived for a model of a classification system beginning with an event set and leading to the final labeling of the event. Functionals on receiver operating characteristic (ROC) curves are developed to form a partial ordering of families of classification ...

On the Continuity of Characteristic Functionals and Sparse Stochastic Modeling

The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic function specifies the probability distribution of its corresponding random variable. Our goal in this work is to lay the foundations of the innovation mode...