Schwartz spaces associated with some non-differential convolution operators on homogeneous groups
S'-convolvability with the Poisson kernel in the Euclidean case and the product domain case
We obtain real-variable and complex-variable formulas for the integral of an integrable distribution in the n-dimensional case. These formulas involve specific versions of the Cauchy kernel and the Poisson kernel, namely, the Euclidean version and the product domain version. We interpret the real-variable formulas as integrals of S’-convolutions. We characterize those tempered distribution that are S’-convolvable with the Poisson kernel in the Euclidean case and the product domain case. As an application...
Semilinear geometric optics for generalized solutions.
Sequence space representations for zero-solutions of convolution equations on ultradifferentiable functions of Roumieu type
Sequence spaces with exponent weights. Realizations of Colombeau type algebras [Book]
Sheaf theory and regularity. Application to local and microlocal analysis
A review of some methods in sheaf theory is presented to make precise a general concept of regularity in algebras or spaces of generalized functions. This leads to the local analysis of the sections of sheaves or presheaves under consideration and then to microlocal analysis and microlocal asymptotic analysis.
Silva distributions for certain locally compact groups.
Silva tempered ultradistributions
Singular perturbations of ordinary differential equations in Colombeau spaces
Singular Products of Distributions.
Singular Products of Distributions.
Singular spectrum of products of distributions at points
Singularités non dégénérées des systèmes de Gauss-Manin réticulés
Slowly decreasing entire functions and convolution equations
Smooth bundles of generalized half-densities
Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Frölicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Frölicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.
Snakes and articulated arms in an Hilbert space
The purpose of this paper is to give an illustration of results on integrability of distributions and orbits of vector fields on Banach manifolds obtained in [5] and [4]. Using arguments and results of these papers, in the context of a separable Hilbert space, we give a generalization of a Theorem of accessibility contained in [3] and [6] for articulated arms and snakes in a finite dimensional Hilbert space.
Sobolev multipliers
Sobolev's and local derivatives
Sobre Ciertos Espacios De Funciones Holo Morfas Y Sus Aplicaciones, II.
Sobre la transformación de Hankel-Schwartz de funciones generalizadas