Let $$F_{\infty }={{\mathbb {F}}_q}\left( \!\left( {1/T}\right) \!\right) $$ be the completion of $${\mathbb {F}}_q(T)$$ at 1/T. We develop a theory Fourier expansions for harmonic cochains on edges Bruhat–Tits building $${{\,\textrm{PGL}\,}}_r(F_{\infty })$$ , $$r\ge 2$$ generalizing an earlier construction Gekeler $$r=2$$ . then apply this to study modular units Drinfeld symmetric space $$\Om...

The purpose of this paper is to find new inclusion relations the harmonic class HF(ϱ,γ) with subclasses SHF*,KHF and TNHF(τ) functions by applying convolution operator Θ(ℑ) associated Mittag-Leffler function. Further for ϱ=0, several special cases main results are also obtained.

In this note we prove a relation between the Riemann Zeta function, ζ and the ξ function (Krein spectral shift) associated with the Harmonic Oscillator in one dimension. This gives a new integral representation of the zeta function and also a reformulation of the Riemann hypothesis as a question in L1(R). ∗Part of talk presented at the Conference on Harmonic Analysis, 13-15 March 1997, Ramanuja...

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number ...

Earlier versions of this software focused on algorithms arising from the material in the book Harmonic Function Theory [ABR] by Sheldon Axler, Paul Bourdon, and Wade Ramey. That book is still the source for many of the algorithms used in the HFT10.m package, but the goal of the package has expanded to include additional symbolic manipulations involving harmonic functions. The HFT10.m package ca...