Convolution Quadrature and Discretized Operational Calculus. I.
Distributional fractional powers of the Laplacean. Riesz potentials
For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of the Laplacean...
Einfache verallgemeinerte klassische Orthogonalpolynome.
Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...
Funciones valoradas (I).
Funciones valoradas (II).
Generalisation of Bell polynomials and related operational formulas.
Generalized Angelescu polynomial
Heaviside's theory of signal transmission on submarine cables
As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values, it has not...
Le papillon de Hofstadter revisité
Linear operators and operational calculus. Part I
Linear operators satisfying the chain rule.
On a variant of the Meijer integral transformation
On some differential and integro-differential equations associated with Jaocobi's differential equation.
On the Meijer transformation.
On the Operational Solution of a System of Fractional Differential Equations
MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and...
On the unification of generalized Hermite and Laguerre polynomials.
Operational calculus and Fourier transform on Boehmians
We define various operations on the space of ultra Boehmians like multiplication with certain analytic functions which are Fourier transforms of compactly supported distributions, polynomials, and characters , translation, differentiation. We also prove that the Fourier transform on the space of ultra Boehmians has all the operational properties as in the classical theory.
Operational calculus for the continuous Legendre transform with applications.