Functions and Analysis

1610 Submissions

[2] viXra:1610.0278 [pdf] submitted on 2016-10-23 16:35:25

Applying the Second Order Two-Scale Approximation to a Dispersive Wave Equation

Authors: Yigal Gurevich
Comments: 8 Pages.

The method of multiple scales is applied and the second order two-scale approximation is calculated for a linear dispersive wave equation with a small perturbation proportional to the amplitude cubed.
Category: Functions and Analysis

[1] viXra:1610.0244 [pdf] submitted on 2016-10-21 04:28:14

Operator Exponentials for the Clifford Fourier Transform on Multivector Fields in Detail

Authors: David Eelbode, Eckhard Hitzer
Comments: 16 Pages. published in Advances in Applied Clifford Algebras, 26(3), pp. 953-968 (2016), Online First: 22 Oct. 2015, DOI: 10.1007/s00006-015-0600-7.

In this paper we study Clifford Fourier transforms (CFT) of multivector functions taking values in Clifford’s geometric algebra, hereby using techniques coming from Clifford analysis (the multivariate function theory for the Dirac operator). In these CFTs on multivector signals, the complex unit i∈C is replaced by a multivector square root of −1, which may be a pseudoscalar in the simplest case. For these integral transforms we derive an operator representation expressed as the Hamilton operator of a harmonic oscillator.
Category: Functions and Analysis