Tauberian and Abelian theorems for rapidly decaying distributions and their applications to stable laws.
Tauberian theorems for generalized functions in the scale of regularly varying functions and functionals.
Tauberian theorems for Laplace transforms.
Tauberian theorems for Laplace transforms in dimension D > 1.
Tauberian theorems for vector-valued Fourier and Laplace transforms
Let X be a Banach space and be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.
The algebra of polynomials on the space of ultradifferentiable functions
We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . A description of the space of polynomial ultradistributions as a locally convex direct sum is given.
The convolution on time scales.
The distributional 1F1-Transform.
The formal Laplace--Borel transform of Fliess operators and the composition product.
The function and some well-known sequences.
The inversion formulae for some Bessel and hypergeometric
The Laplace derivative
A function is said to have the -th Laplace derivative on the right at if is continuous in a right neighborhood of and there exist real numbers such that converges as for some . There is a corresponding definition on the left. The function is said to have the -th Laplace derivative at when these two are equal, the common value is denoted by . In this work we establish the basic properties of this new derivative and show that, by an example, it is more general than the generalized...
The Laplace transform of analytic vector-valued functions (complex conditions)
The Laplace transform of exponentially bounded vector-valued functions (real conditions)
The Laplace transform of the modified Bessel function of the second kind.
The Laplace transform on a Boehmian space
In the literature a Boehmian space containing all right-sided Laplace transformable distributions is defined and studied. Besides obtaining basic properties of this Laplace transform, an inversion formula is also obtained. In this paper we shall improve upon two theorems one of which relates to the continuity of this Laplace transform and the other is concerned with the inversion formula.
The non-Archimedean Laplace transform.
The Numerical Performance of Tricomi's Formula for Inverting the Laplace Transform.
The operator remainder in the Euler-Maclaurin formula.
The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation.