This section deals with the definition, terminologies, and properties of the Sumudu transform and the Abel integral equation. In Section 2, solution of Abel integral equation is obtained by the application of the Sumudu transform, and in Section 3, the Sumudu transform is proved for distribution spaces, and the solution of Abel integral equation in the sense of distribution is obtained. The Sum...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

The present paper provides exact expressions for the probability distribution of linear functionals of the two–parameter Poisson–Dirichlet process PD(α, θ). Distributional results that follow from the application of an inversion formula for a (generalized) Cauchy– Stieltjes transform are achieved. Moreover, several interesting integral identities are obtained by exploiting a correspondence betw...

The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information theory, machine learning, and statistics. In particular, k-nearest neighbor (nn) based methods have received a lot of attention due to their adaptive nature an...

Introduction. The primary purpose of this note is to construct a C* Lyapunov function for a continuous vector field which has an asymptotically stable invariant set. Since there already exist techniques for constructing continuous Lyapunov functions with continuous derivatives by the vector field, our problem is simply to smooth such a function in such a way that the desired derivative properti...

The existence of distributional solutions is investigated for the time-dependent bending of a plate with transverse shear deformation under mixed boundary conditions. The problem is then reduced to nonstationary boundary integral equations and the existence and uniqueness of solutions to the latter are studied in appropriate Sobolev spaces. 2000 Mathematics Subject Classification: 74H20, 74K20,...

We study in distributional sense by means of the kernel method an integral transform introduced by Krätzel. It is well known that the cited transform generalizes to the Laplace and Meijer transformation. Properties of analyticity, boundedness, and inversion theorems are established for the generalized transformation. 2000 Mathematics Subject Classification. Primary 44A15, 46F12.