Calculation of the Bidual for Some Function Spaces. Integrable Distributions.
Caratterizzazione dei polinomi di convoluzione in una variabile a decrescenza rapida, a coefficienti costanti, che hanno soluzioni quasi periodiche per ogni termine noto quasi periodico
Cauchy-Kowalewski extension theorems and representations of analytic functionals acting over special classes of real n-dimensional submanifolds of
Cauchy's problem for systems of linear differential equations with distributional coefficients
Characterization of Convolution Operators on Spaces of C-Functions Admitting a Continuous Linear Right Inverse.
Characterization of Hankel transformable generalized functions.
Characterization of Mellin distributions supported by certain noncompact sets
A class of distributions supported by certain noncompact regular sets K are identified with continuous linear functionals on . The proof is based on a parameter version of the Seeley extension theorem.
Characterization of regular tempered distributions
Characterization of some Subspaces of (D') by S-asymptotic
Characterization of surjective convolution operators on Sato's hyperfunctions
Let be an analytic functional and let be the corresponding convolution operator on Sato’s space of hyperfunctions. We show that is surjective iff admits an elementary solution in iff the Fourier transform μ̂ satisfies Kawai’s slowly decreasing condition (S). We also show that there are such that is not surjective on .
Characterization of surjective partial differential operators on spaces of real analytic functions
Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves previous...
Characterization of the Colombeau product of distributions
Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse
Solving a problem of L. Schwartz, those constant coefficient partial differential operators are characterized that admit a continuous linear right inverse on or , an open set in . For bounded with -boundary these properties are equivalent to being very hyperbolic. For they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial .
Characterization of the range of the Radon transform on homogeneous trees.
Characterization of the hypoelliptic convolution operators on ultradistributions.
Classes du type Sobolev
Classes de protenseurs distributions contravariants
Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives
This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...
Coefficients généralisés de séries principales sphériques et distributions sphériques sur G.../G... .
Colombeau product of currents
Colombeau product of de Rham's currents coincides with generalized Itano one. Sufficient conditions are found under which it is diffeomorphism invariant.