Hybrid Transforms of Constructible Functions

Radon transforms of Constructible functions on Grassmann manifolds

In [14], P.Schapira obtained a formula for RS in the general situation. This formula gives an inversion formula for the Radon transform of constructible functions from a real projective space to its dual in the case when the whole dimension is odd. We can, that is, reconstruct a constructible function φ on the projective space from its Radon transform RS(φ). This topological meaning is that we ...

Algebraically Constructible Functions

An algebraic version of Kashiwara and Schapira's calculus of constructible functions is used to describe local topological properties of real algebraic sets, including Akbulut and King's numerical conditions for a stratiied set of dimension three to be algebraic. These properties, which include generalizations of the invariants modulo 4, 8, and 16 of Coste and Kurdyka, are deened using the link...

Description of algebraically constructible functions

The algebraically constructible functions on a real algebraic set are the sums of signs of polynomials on this set. We prove a formula giving the minimal number of polynomials needed to write generically a given algebraically constructible function as a sum of signs. We also prove a characterization of the polynomials appearing in a generic presentation of the function with the minimal number o...

Algebraically Constructible Functions and Signs of Polynomials

Let W be a real algebraic set. We show that the following families of integervalued functions on W coincide: (i) the functions of the form w → χ(Xw), where Xw are the fibres of a regular morphism f : X → W of real algebraic sets, (ii) the functions of the form w → χ(Xw), where Xw are the fibres of a proper regular morphism f : X →W of real algebraic sets, (iii) the finite sums of signs of polyn...

The Fekete-Szego Coefficient Functional for Transforms of Analytic Functions