Sampling expansions associated with quaternion difference equations
Classical Analysis and ODEs
2022-09-20 v2
Abstract
Starting with a quaternion difference equation with boundary conditions, a parameterized sequence which is complete in finite dimensional quaternion Hilbert space is derived. By employing the parameterized sequence as the kernel of discrete transform, we form a quaternion function space whose elements have sampling expansions. Moreover, through formulating boundary-value problems, we make a connection between a class of tridiagonal quaternion matrices and polynomials with quaternion coefficients. We show that for a tridiagonal symmetric quaternion matrix, one can always associate a quaternion characteristic polynomial whose roots are eigenvalues of the matrix. Several examples are given to illustrate the results.
Cite
@article{arxiv.1903.05540,
title = {Sampling expansions associated with quaternion difference equations},
author = {Dong Cheng and Kit Ian Kou and Yonghui Xia and Junfeng Xu},
journal= {arXiv preprint arXiv:1903.05540},
year = {2022}
}