IKKINCHI TIP KLASSIK SOHALARDA LAPLAS ALMASHTIRISHI, TESKARI LAPLAS ALMASHTIRISH FORMULASI VA TASVIR FUNKSIYANING GOLOMORFLIGI HAQIDAGI TEOREMANING ANALOGI

In this article, we will consider the basic concepts of operational calculus, the connections between images
and original functions, in particular, the Laplace transform, the inverse Laplace transform, and one of its
important theorems, namely the theorem on the holomorphism of a matrix image function, for classical domains
of the second type. To do this, we first introduce the basic definitions and concepts. It is known that classical
domains do not have a biholomorphic equivalence relation with each other, therefore, a complex analysis is
constructed separately for each of them. Therefore, in this article, we will only deal with obtaining analogues of
the Laplace transform in classical domains of the second type, which belong to the class of symmetric Hermitian
matrices. In our further scientific research, we will try to obtain analogues of the Laplace transform for matrixfunctions
belonging to the class of rectangular matrices of the first type and the class of antisymmetric matrices
of the third type.