SOME THEOREMS ON A GENERALIZED LAPLACE TRANSFORM OF GENERALIZED FUNCTIONS

Laplace Transformation on Ordered Linear Space of Generalized Functions

Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L′(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounde...

Some Asymptotic Formulas on Generalized Divisor Functions

1 . Throughout this paper, we use the following notation : c•1 , c2 , . . ., X0 , X1 , . . . denote positive absolute constants. We denote the number of elements of the finite set S by BSI . We write ex =exp (x) . We denote the least prime factor of n by p(n) . We write pall n if pain but pa+1 f n . v(n) denotes the number of the distinct prime factors of n, while the number of all the prime fa...

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.

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,,...

Some results on a generalized ω-Jacobi transform