The purpose of this text is to introduce family of generalized function associated to quadratic form depending of analytic parameter so that they can be applied to problem for partial differential equation. In this book we are going to study several distributional family with real coefficients and complex coeffients. In particular taking into account that μ+ν=n dimension of the space, we are going to study the quadratic form taking into account that i=1,2, ...μ and i=μ+1, ...μ+ν The mains results appearent in the chapters: 3,4,5,6,7,8. In this text appear generalization of property of elliptic kernel of Marcel Riesz and generalization formulae that appear in the text of Gelfand and Shilov ( Generalized Functions, vol.I, Acdemic Press, 1964) . On the other hand we obtain generalization of Nozaki ultrahyperbolic kernel and generalization of distribution family W(u, c) defined in the chapte