A dynamic matrix exponential via a matrix cylinder transformation

Authors

Tom Cuchta, Marshall UniversityFollow
David Grow
Nick Wintz

Document Type

Article

Publication Date

11-2019

Abstract

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.

Comments

Copyright © 2019 Elsevier Inc. All rights reserved.

Recommended Citation

Cuchta, T., Grow, D., & Wintz, N. (2019). A dynamic matrix exponential via a matrix cylinder transformation. Journal of Mathematical Analysis and Applications, 479(1), 733-751.