Sur une classe d'algèbre de fonctions généralisées application aux systèmes différentiels
Sur une définition de la valeur d'une distribution en un point et son application au problème de Cauchy
Sur une méthode de resolution de l’équation
Sur une notion de limite d'une ultradistribution en un point. I
Sur une notion de limite d'une ultradistribution en un point. II
Surjective convolution operators on spaces of distributions.
We review recent developments in the theory of inductive limits and use them to give a new and rather easy proof for Hörmander?s characterization of surjective convolution operators on spaces of Schwartz distributions.
Surjectivity of convolution operators on spaces of ultradifferentiable functions of Roumieu type
Let denote the space of all ω-ultradifferentiable functions of Roumieu type on an open interval I in ℝ. In the special case ω(t) = t we get the real-analytic functions on I. For with one can define the convolution operator , . We give a characterization of the surjectivity of for quasianalytic classes , where I = ℝ or I is an open, bounded interval in ℝ. This characterization is given in terms of the distribution of zeros of the Fourier Laplace transform of μ.
Surjectivity of partial differential operators on ultradistributions of Beurling type in two dimensions
We show that if Ω is an open subset of ℝ², then the surjectivity of a partial differential operator P(D) on the space of ultradistributions of Beurling type is equivalent to the surjectivity of P(D) on .
Systems of convolution equations and LAU-spaces
Dato un sistema omogeneo di equazioni di convoluzione in spazi dotati di strutture analiticamente uniformi, si forniscono condizioni per ottenere teoremi di rappresentazione per le sue soluzioni.
Taylor formula for distributions [Book]
Taylor-type expansion of the -th derivative of the Dirac delta in .
Tempered nontangential boundedness
The algebra of polynomials on the space of ultradifferentiable functions
We consider the space of ultradifferentiable functions with compact supports and the space of polynomials on . A description of the space of polynomial ultradistributions as a locally convex direct sum is given.
The distributional multiplicative product P ...
The divergent distribution product Xλ+Xμ-.
The domain of attraction of a normal distribution in a Hilbert space
The Fourier transform in Lebesgue spaces
For each () it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to . There is an exchange theorem and inversion in norm.
The Fourier transform of distributions and the exchange formula
The Kontorovich-Lebedev Transformation of Distributions.
The linear Cauchy problem for a class of differential equations with distributional coefficients.