EuDML | Browse

A function $f : ℝ \to ℝ$ is said to have the $n$ -th Laplace derivative on the right at $x$ if $f$ is continuous in a right neighborhood of $x$ and there exist real numbers $α_{0}, ..., α_{n - 1}$ such that $s^{n + 1} \int_{0}^{δ} e^{- s t} [f (x + t) - \sum_{i = 0}^{n - 1} α_{i} t^{i} / i!] d t$ converges as $s \to + \infty$ for some $δ > 0$ . There is a corresponding definition on the left. The function is said to have the $n$ -th Laplace derivative at $x$ when these two are equal, the common value is denoted by $f_{〈 n 〉} (x)$ . 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)

Miroslav Sova (1979)

Časopis pro pěstování matematiky

The Laplace transform of exponentially bounded vector-valued functions (real conditions)

Miroslav Sova (1980)

Časopis pro pěstování matematiky

The Laplace transform of the modified Bessel function of the second kind.

H.M. Srivastava (1979)

Publications de l'Institut Mathématique [Elektronische Ressource]

The Laplace transform on a Boehmian space

V. Karunakaran, C. Prasanna Devi (2010)

Annales Polonici Mathematici

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 $_{2} F_{1}$ -transform

Benito J. González, Emilio R. Negrin (1996)

Commentationes Mathematicae Universitatis Carolinae

In this note we show that the two definitions of generalized index $_{2} F_{1}$ -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.

Nasim, Cyril (1984)

International Journal of Mathematics and Mathematical Sciences

The Meilin Transform of the Partial Fraction Expansion for 0 (x).

P.L. Walker (1980)

Mathematische Annalen

The Mejer transformation of generalized functions.

Koh, E.L., Deeba, E.Y., Ali, M.A. (1987)

International Journal of Mathematics and Mathematical Sciences

The modified Cauchy transformation with applications to generalized Taylor expansions

Bogdan Ziemian (1992)

Studia Mathematica

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.

Currently displaying 41 – 60 of 103

Previous Page 3 Next

Displaying 41 – 60 of 103

The Identification Problem for the Constantly Attenuated Radon Transform.

The inversion formulae for some Bessel and hypergeometric

The Invertibility of the Radon Transform on Abstract Rotational Manifolds of Real Type.

The K-moment problem for compact semi-algebraic sets.

The $L^{2}$ -optimal convolving functions in reconstruction convolution algorithms

The $L^{p}$ mapping problem for well-behaved convolutions

The Lambert transform on $ε^{'} (I)$

The Laplace derivative