An approach to generalized holomorphic functions

A study of the generalized holomorphic functions, HG(Omega), having in mind its strict elements, i.e. those which are in HG(Omega) - H(Omega), as well as the possibility of the existence of hybrid elements, i.e. elements which have, in a part of a domain Omega subset of C-n, the strict behaviour and, in another part of the same domain, the classical behaviour, is carried out in this work. The study of hybrid elements is important in the approach of a concept of generalized domain of holomorphy.

On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Algebraic properties of Rogers-Szego functions: I. Applications in quantum optics

By means of a well-established algebraic framework, Rogers-Szego functions associated with a circular geometry in the complex plane are introduced in the context of q-special functions, and their properties are discussed in detail. The eigenfunctions related to the coherent and phase states emerge from this formalism as infinite expansions of Rogers-Szego functions, the coefficients being determined through proper eigenvalue equations in each situation. Furthermore, a complementary study on the Robertson-Schrodinger and symmetrical uncertainty relations for the cosine, sine and nondeformed number operators is also conducted, corroborating, in this way, certain features of q-deformed coherent states.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset �� of ���n, there is a differential algebra G(��) of generalized functions which contains in a natural way the space D���(��) of distributions as a vector subspace. There is also a simpler version of the algebra G,(��). Although this subalgebra does not contain, in canonical way, the space D���(��) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

LOGO2VHDL: modelos descritos em VHDL a partir da linguagem do LOGO!Soft Comfort da Siemens

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

C��lculo fracion��rio aplicado em din��mica tumoral: m��todo da Transformada Diferencial generalizada

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

Schur-SzegA composition of entire functions

Funda����o de Amparo �� Pesquisa do Estado de S��o Paulo (FAPESP)

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. �� 1997 American Institute of Physics.

Massless scattering at special kinematics as Jacobi polynomials

We study the scattering equations recently proposed by Cachazo, He and Yuan in the special kinematics where their solutions can be identified with the zeros of the Jacobi polynomials. This allows for a non-trivial two-parameter family of kinematics. We present explicit and compact formulas for the n-gluon and n-graviton partial scattering amplitudes for our special kinematics in terms of Jacobi polynomials. We also provide alternative expressions in terms of gamma functions. We give an interpretation of the common reduced determinant appearing in the amplitudes as the product of the squares of the eigenfrequencies of small oscillations of a system whose equilibrium is the solutions of the scattering equations.

INTEGRAL FUNCTIONALS ON C*-ALGEBRA OF VECTOR-VALUED REGULATED FUNCTIONS

In this paper we deal with the notion of regulated functions with values in a C*-algebra A and present examples using a special bi-dimensional C*-algebra of triangular matrices. We consider the Dushnik integral for these functions and shows that a convenient choice of the integrator function produces an integral homomorphism on the C*-algebra of all regulated functions ([a, b], A). Finally we construct a family of linear integral functionals on this C*-algebra.

Schur-Szeg�� composition of entire functions

Funda����o de Amparo �� Pesquisa do Estado de S��o Paulo (FAPESP)