arXiv subjects
Publications and source records attributed to Radu Paltanea.
In the present paper, we study the asymptotic properties of the semi-exponential Post-Widder operator. It is connected with $p(x) = x^2$. The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. As a special case we recover the complete asymptotic expansion for the classical Post-Widder operator.
In this article we study a generalization of the n-inner product which we name weak n-inner product. As particular case we consider the n-iterated 2-inner product and we give its representation in terms of the standard k-inner products, k<= n, using the Dodgson's identity for determinants. Finally, we present several applications, including a brief characterization of a linear regression model for the random variables in discrete case and a generalization of the Chebyshev functional using the n-iterated 2-inner product.