Bessel matrix differential equations: explicit solutions of initial and two-point boundary value problems
Volume 22 / 1993
Applicationes Mathematicae 22 (1993), 11-23
DOI: 10.4064/am-22-1-11-23
Abstract
In this paper we consider Bessel equations of the type $t^2 X^{(2)}(t) + t X^{(1)}(t) + (t^2 I - A^2)X(t) = 0$, where A is an n$\times$n complex matrix and X(t) is an n$\times$m matrix for t > 0. Following the ideas of the scalar case we introduce the concept of a fundamental set of solutions for the above equation expressed in terms of the data dimension. This concept allows us to give an explicit closed form solution of initial and two-point boundary value problems related to the Bessel equation.
