We provide a simple construction for a matrix representation of the Gale transform of a simplotope, the Cartesian product of simplices. The matrix representation is a Kronecker product of matrices representing the Gale transforms of the component simplices. We also show that Hadamard matrices occur as a special case of this construction.

—We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic function and determine all infinitely divisible probability measures on the unit circle for the boolean convolution. Résumé (Convolution booléenne de probab...

We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive convolution μ` ν of compactly supported probability measures in free probability. These decompositions are directly related to alternating decompositions of the ...

Space-varying convolution often arises in the modeling or restoration of images captured by optical imaging systems. For example, in applications such as microscopy or photography the distortions introduced by lenses typically vary across the field of view, so accurate restoration also requires the use of space-varying convolution. While space-invariant convolution can be efficiently implemente...

We prove some general theorems which unify results on arithmetic-geometric mean and some other related matrix inequalities. As an application we obtain some results involving Hadamard product of matrices. Mathematics subject classification (2010): 47A30 15A60.

Nomenclature Hadamard product k k2, k kF spectral norm, Frobenius norm 0l m; 0l l m zero matrix, 0l l Il; 1l m l l identity matrix, l m ones matrix

By making use of the Hadamard product, we define a new class of analytic functions of complex order. Coefficient inequalities, sufficient condition and an interesting subordination result are obtained. 2000 Mathematics Subject Classification: 30C45, 30C50.

The product of two free scalar fields on a manifold is shown to be a well defined operator valued distribution on the GNS Hilbert space of a globally Hadamard product state. Viewed as a new field all n-point distributions exist, giving a new example for a Wightman field on a manifold.