A Dynamic Matrix Exponential Via a Matrix Cylinder Transformation
In this work, we develop a new matrix exponential on time scales via a cylinder transformation with a component-wise, locally µΔ-integrable square matrix subscript. Our resulting matrix function can be written in terms of the matrix exponential of a Lebesgue integral added to a logarithmic sum in terms of the gaps of a general time scale. Under strict commutativity conditions, we show our dynamic matrix exponential is equivalent to the one in the standard literature. Finally, we demonstrate that our matrix exponential satisfies a nonlinear dynamic integral equation.
T. Cuchta et al., "A Dynamic Matrix Exponential Via a Matrix Cylinder Transformation," Journal of Mathematical Analysis and Applications, vol. 479, no. 1, pp. 733 - 751, Academic Press Inc., Nov 2019.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2019.06.048
Mathematics and Statistics
Keywords and Phrases
Cylinder transformation; Matrix exponential; Time scales calculus
International Standard Serial Number (ISSN)
Article - Journal
© 2019Elsevier Inc., All rights reserved.
01 Nov 2019