We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman–Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler–Heine formula, that is an approximation of the Heckman–Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This ...

The main result is that any continuous real-linear operator A on a quaternionic Hubert space has a unique decomposition A=A0+iiAl + izAi+iiA3, where the A„ are continuous linear operators and (fi,f2,'3) is any right-handed orthonormal triad of vector quaternions. Other results concern the place of the colinear and complex-linear operators in this characterisation and the effect on the Av of a r...

Using the complex Klein-Gordon field as a model, we quantize quaternionic scalar in real Hilbert space. The lagrangian formulation has accordingly been obtained, well hamiltonian formulation, and energy charge operators. Conversely to case, quantization admits two schemes, concerning either or four components. Therefore, permits richer structure of states, if compared case. Moreover, theory fur...

The real-quaternionic indicator, also called the δ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely connected to the Frobenius-Schur indicator, which we call the ε indicator. It is interesting to compute the ε and δ indicators. The computation of the ε indicator is relatively straightforward. In fact, it has been proven in large generality t...

The analytic signal of a real signal is a standard concept in 1D signal processing. However, the deenition of an analytic signal for real 2D signals is not possible by a straightforward extension of the 1D deenition. There rather occur several diierent approaches in the literature. We review the main approaches and propose a new deenition which is based on the recently introduced quaternionic F...