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arXiv · 1903.05540

Sampling expansions associated with quaternion difference equations

Dong Cheng·Kit Ian Kou·Yonghui Xia·Junfeng Xu
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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.

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Dong Cheng, Kit Ian Kou, Yonghui Xia, Junfeng Xu. 2019-03-13. Sampling expansions associated with quaternion difference equations. https://doi.org/10.1080/03081087.2022.2094863

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