The -optimal convolving functions in reconstruction convolution algorithms
The mapping problem for well-behaved convolutions
The Lambert transform on
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 link between the kernel method and the method of adjoints for the generalized index -transform
In this note we show that the two definitions of generalized index -transform given in the previous works [1] and [2] agree for distributions of compact support.
The Mehler-Fock transform of general order and arbitrary index and its inversion.
The Meilin Transform of the Partial Fraction Expansion for 0 (x).
The Mejer transformation of generalized functions.
The modified Cauchy transformation with applications to generalized Taylor expansions
We generalize to the case of several variables the classical theorems on the holomorphic extension of the Cauchy transforms. The Cauchy transformation is considered in the setting of tempered distributions and the Cauchy kernel is modified to a rapidly decreasing function. The results are applied to the study of "continuous" Taylor expansions and to singular partial differential equations.
The moment problem for non-compact semialgebraic sets.
The Moment Problem in the Space C... (S).
The multidimensional -transform and its use in solution of partial difference equations
The n-dimensional distributional Mellin transformation.
The Neutrix Convolution Product x -r,- ○ x μ,+
The non-Archimedean Laplace transform.
The Numerical Performance of Tricomi's Formula for Inverting the Laplace Transform.