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.
The Singularity Expansion Method applied to the transient motions of a floating elastic plate
In this paper we propose an original approach for the simulation of the time-dependent response of a floating elastic plate using the so-called Singularity Expansion Method. This method consists in computing an asymptotic behaviour for large time obtained by means of the Laplace transform by using the analytic continuation of the resolvent of the problem. This leads to represent the solution as the sum of a discrete superposition of exponentially damped oscillating motions associated to the poles...
The space of Laplace transformable distributions
The -transformation on McBride’s spaces of generalized functions
An integral transform denoted by that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.
Theorem on association of variables in multidimensional Laplace transforms.
Theorems on -dimensional Laplace transforms and their applications.
Theorems on some families of fractional differential equations and their applications
We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration...
Time-Fractional Derivatives in Relaxation Processes: A Tutorial Survey
2000 Mathematics Subject Classification: 26A33, 33E12, 33C60, 44A10, 45K05, 74D05,The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the Caputo sense. After giving a necessary outline of the classica theory of linear viscoelasticity, we contrast these two types of fractiona derivatives in their ability to take into...
Transfer of connection problems for first level solutions of merimorphic differential equations, and associated Laplace transforms.
Transformations de Laplace et de Mellin. Formulaires. Mode d'utilisation [Book]
Transformations de Laplace sur des sous-variétés de et représentations d’ondes entrantes et sortantes
Two dimensional Laplace transforms of generalized hypergeometric functions.
Weighted inequalities through factorization.
In [4] P. Jones solved the question posed by B. Muckenhoupt in [7] concerning the factorization of Ap weights. We recall that a non-negative measurable function w on Rn is in the class Ap, 1 < p < ∞ if and only if the Hardy-Littlewood maximal operator is bounded on Lp(Rn, w). In what follows, Lp(X, w) denotes the class of all measurable functions f defined on X for which ||fw1/p||Lp(X) < ∞, where X is a measure space and w is a non-negative measurable function on X.It has recently...
When is a Riesz distribution a complex measure?
Let be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by . I give an elementary proof of the necessary and sufficient condition for to be a locally finite complex measure (= complex Radon measure).
Zeros and regular growth of Laplace transforms along curves.
Zeros of smallest modulus of functions resembling exp(z).
Zur numerischen Inversion von Laplace Transformierten
α-Mellin Transform and One of Its Applications
MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin transform...
Банаховы алгебры мер на прямой, связанные с асимптотическим поведением мер на бесконечности.