Generalized Laplace transform with matrix variables

The Capelli Identity, Tube Domains, and the Generalized Laplace Transform*

The key result in this paper is a proof of a large class of identities, generalizing the Capelli identity [Cl. The Capelli identity is a centerpiece of 19th century invariant theory. It asserts the equality of two differential operators on the n2-dimensional space M(n, R) of n x n real matrices. Let E, denote the ijth elementary matrix, let xii denote the linear functions on M(n, R) dual to E,,...

Laplace Transform

We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...

On the Laplace Transform of the State Transition Matrix

This note presents the explicit form of the Laplace transform of the state transition matrix in the case of a system matrix being a companion matrix. Starting from this special case, we show how to compute the Laplace transform of the state transition matrix for any system matrix.1

Asymmetric Univariate and Bivariate Laplace and Generalized Laplace Distributions

Alternative specifications of univariate asymmetric Laplace models are described and investigated. A more general mixture model is then introduced. Bivariate extensions of these models are discussed in some detail, with particular emphasis on associated parameter estimation strategies. Multivariate versions of the models are briefly introduced.

Generalized Pascal k-eliminated functional matrix with 2n variables