Abstract. It is shown that a broad class of generalized Dirichlet series (including the polylogarithm, related to the Riemann zeta-function) can be presented as a class of solutions of the Fourier transformed spatially homogeneous linear Boltzmann equation with a special Maxwell-type collision kernel. The result is based on an explicit integral representation of solutions to the Cauchy problem ...

Euclidean Clifford analysis is a higher dimensional function theory offering a refinement of classical harmonic analysis. The theory is centred around the concept of monogenic functions, which constitute the kernel of a first order vector valued, rotation invariant, differential operator ∂ called the Dirac operator, which factorizes the Laplacian. More recently, Hermitean Clifford analysis has ...

Matched filters are the optimal linear filters for signal detection under linear channel and white noise conditions. Their optimality is guaranteed in the additive white Gaussian noise channel due to the sufficiency of second order statistics. In this paper, we introduce a nonlinear filter for signal detection based on the Cauchy-Schwartz quadratic mutual information (CS-QMI) criterion. This fi...

In this paper, a novel matched filter based on a new kernel function with Cauchy distribution is introduced to improve the accuracy of the automatic retinal vessel detection compared with other available matched filter-based methods, most notably, the methods built on Gaussian distribution function. Several experiments are conducted to pick the best values of the parameters for the new designed...

Let = G=K be a bounded symmetric domain in a complex vector space V with the Lebesgue measure dm(z) and the Bergman reproducing kernel h(z; w) ?p. Let dd (z) = h(z; z) dm(z), > ?1, be the weighted measure on. The group G acts unitarily on the space L 2 ((;) via change of variables together with a multiplier. We consider the discrete parts, also called the relative discrete series, in the irredu...