Functions and Analysis

1407 Submissions

[3] viXra:1407.0169 [pdf] submitted on 2014-07-21 15:55:09

New Developments in Clifford Fourier Transforms

Authors: Eckhard Hitzer
Comments: 7 Pages. in N. E. Mastorakis, P. M. Pardalos, R. P. Agarwal, L. Kocinac (eds.), Adv. in Appl. and Pure Math., Proc. of the 2014 Int. Conf. on Pure Math., Appl. Math., Comp. Methods (PMAMCM 2014), Santorini, Greece, July 2014, Math. & Comp. in Sci. & Eng., Vol. 29.

We show how real and complex Fourier transforms are extended to W.R. Hamilton's algebra of quaternions and to W.K. Clifford’s geometric algebras. This was initially motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of applications in color image and signal processing. Clifford's geometric algebras are complete algebras, algebraically encoding a vector space and all its subspace elements. Applications include electromagnetism, and the processing of images, color images, vector field and climate data. Further developments of Clifford Fourier Transforms include operator exponential representations, and extensions to wider classes of integral transforms, like Clifford algebra versions of linear canonical transforms and wavelets.
Category: Functions and Analysis

[2] viXra:1407.0054 [pdf] submitted on 2014-07-07 18:13:59

Semicontinuous Filter Limits of Nets of Lattice Group-Valued Functions

Authors: Antonio Boccuto, X. Dimitriou
Comments: 4 Pages.

Some conditions for semicontinuity of the limit function of a pointwise convergent net of lattice group-valued functions with respect to filter convergence are given. In this framework we consider some kinds of filter exhaustiveness.
Category: Functions and Analysis

[1] viXra:1407.0044 [pdf] submitted on 2014-07-05 12:22:07

Strong Uniform Continuity and Filter Exhaustiveness of Nets of Cone Metric Space-Valued Functions

Authors: Antonio Boccuto, Xenofon Dimitriou
Comments: 3 Pages.

We give necessary and sufficient conditions for (strong uniform) continuity of the limit of a pointwise convergent net of cone metric space-valued functions. In this framework we consider several types of convergence in the filter context and some kinds of filter exhaustiveness.
Category: Functions and Analysis