New properties of the Laplace transform in the classical domains of second type

In this work, matrix analogues of the general properties of the Laplace transform for the classical domains of second type were established. In particular, the theorem on the holomorphicity of the image function, the uniqueness theorem for original function, and an explicit inverse Laplace transform formula were derived in the matrix setting. Furthermore, new properties specific to the classical domains of second type were obtained and rigorously proved using direct matrix differential operators.