A ug 2 00 6 Associated and quasi associated homogeneous distributions ( generalized functions )
نویسندگان
چکیده
In this paper analysis of the concept of associated homogeneous distributions (generalized functions) is given, and some problems related to these distributions are solved. It is proved that (in the one-dimensional case) there exist only associated homogeneous distributions of order k = 1. Next, we introduce a definition of quasi associated homogeneous distributions and provide a mathematical description of all quasi associated homogeneous distributions and their Fourier transform. It is proved that the class of quasi associated homogeneous distributions coincides with the class of distributions introduced by Gelfand and Shilov [6, Ch.I,§4.] as the class of associated homogeneous distributions. For the multidimensional case it is proved that f is a quasi associated homogeneous distribution if and only if it satisfies the Euler type system of differential equations. A new type of Γ-functions generated by quasi associated homogeneous distributions is defined.
منابع مشابه
7 A ug 2 00 6 THE MODULI SPACE OF N = 2 SUPER - RIEMANN SPHERES WITH TUBES
Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N = 2 superconformal field theory , we define the moduli space of N = 2 super-Riemann spheres with oriented and ordered half-infinite tubes (or equivalently, oriented and ordered punctures, and local superconformal coordinates vanishing at the punctures), modulo N = 2 superconformal equivalence...
متن کامل2 00 6 Algebraic computation of some intersection D - modules
Let X be a complex analytic manifold, D ⊂ X a locally quasi-homogeneous free divisor, E an integrable logarithmic connection with respect to D and L the local system of the horizontal sections of E on X − D. In this paper we give an algebraic description in terms of E of the regular holonomic DX-module whose de Rham complex is the intersection complex associated with L. As an application, we pe...
متن کامل2 5 A ug 2 00 8 Asymptotical behavior of one class of p - adic singular Fourier integrals
We study the asymptotical behavior of the p-adic singular Fourier integrals Jπα,m;φ(t) = 〈 fπα;m(x)χp(xt), φ(x) 〉 = F [ fπα;mφ ] (t), |t|p → ∞, t ∈ Qp, where fπα;m ∈ D ′(Qp) is a quasi associated homogeneous distribution (generalized function) of degree πα(x) = |x| α−1 p π1(x) and orderm, πα(x), π1(x), and χp(x) are a multiplicative, a normed multiplicative, and an additive characters of the fi...
متن کامل