Fourier inversion formula for discrete nilpotent groups

A Fourier Inversion Formula for Evolutionary Trees

We establish a pair of identities, which will provide a useful tool in the reconstruction of evolutionary trees in Kimura's 3-parameter model. The starting point of this paper was an attempt for a better understanding and generalization of an Hadamard inverse pair of formulae, which was used in statistics by Cooper [l], in image processing by Andrews [2, Chapters 6,7], and in information theory...

Discrete Fourier Inversion of Linear Inhomogeneity

Solutions to tensor, vector, and scalar linear inhomogeneous partial differential equations can be obtained by discrete Fourier inversion of the linear system. The inverse (Green’s function) problem can be cast into sets of single, double, and triple summation/integration expressions by using transcendental eigenfunction expansions in certain three-dimensional triply-orthogonal geometries whose...

Nilpotent Groups

The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

An Abramov Formula for Stationary Spaces of Discrete Groups

Let (G,μ) be a discrete group equipped with a generating probability measure, and let Γ be a finite index subgroup of G. A μ-random walk on G, starting from the identity, returns to Γ with probability one. Let θ be the hitting measure, or the distribution of the position in which the random walk first hits Γ. We prove that the Furstenberg entropy of a (G,μ)-stationary space, with respect to the...