1,474 research outputs found
Lost in transition? A comparison of early drop out from education and training in England and France
Polyanalytic Hardy decomposition of higher order Lipschitz functions
This paper is concerned with the problem of decomposing a higher order
Lipschitz function on a closed Jordan curve into a sum of two
polyanalytic functions in each open domain defined by . Our basic tools
are the Hardy projections related to a singular integral operator arising in
polyanalytic function theory, which, as it is proved here, represents an
involution operator on the higher order Lipschitz classes. Our result
generalizes the classical Hardy decomposition of Holder continuous functions on
the boundary of a domain
Hermitian clifford analysis
This paper gives an overview of some basic results on Hermitian Clifford analysis, a refinement of classical Clifford analysis dealing with functions in the kernel of two mutually adjoint Dirac operators invariant under the action of the unitary group. The set of these functions, called Hermitian monogenic, contains the set of holomorphic functions in several complex variables. The paper discusses, among other results, the Fischer decomposition, the Cauchy–Kovalevskaya extension problem, the axiomatic radial algebra, and also some algebraic analysis of the system associated with Hermitian monogenic functions. While the Cauchy–Kovalevskaya extension problem can be carried out for the Hermitian monogenic system, this system imposes severe constraints on the initial Cauchy data. There exists a subsystem of the Hermitian monogenic system in which these constraints can be avoided. This subsystem, called submonogenic system, will also be discussed in the paper
On a Generalized Lam\'e-Navier system in
This paper is devoted to a fundamental system of equations in Linear
Elasticity Theory: the famous Lam\'e-Navier system. The Clifford algebra
language allows us to rewrite this system in terms of the euclidean Dirac
operator, which at the same time suggests a very natural generalization
involving the so-called structural sets. We are interested in finding some
structures in the solutions of these generalized Lam\'e-Navier systems. Using
MATLAB we also implement algorithms to compute with such partial differential
operators as well as to verify some theoretical results obtained in the paper.Comment: 19 pages 0 figure
Duality for Hermitean systems in R2n
In this paper, using the algebraic structure of the space of circulant (2 × 2) matrix, we characterize the dual of the (Frechet) space of germs of left Hermitean monogenic matrix functions in a compact set of Euclidean space with even di;ension. As an application we describe the dual space of the so-called h-monogenic functions satisfying simultaneously two Dirac type equations
Generalized Moisil-Théodoresco systems and Cauchy integral decompositions
Let ℝ0,m+1(s) be the space of s-vectors (0≤s≤m+1) in the Clifford algebra ℝ0,m+1 constructed over the quadratic vector space ℝ0,m+1, let r,p,q∈ℕ with 0≤r≤m+1, 0≤p≤q, and r+2q≤m+1, and let ℝ0,m+1(r,p,q)=∑j=pq⨁ ℝ0,m+1(r+2j). Then, an ℝ0,m+1(r,p,q)-valued smooth function W defined in an open subset Ω⊂ℝm+1 is said to satisfy the generalized Moisil-Théodoresco system of type (r,p,q) if ∂xW=0 in Ω, where ∂x is the Dirac operator in ℝm+1. A structure theorem is proved for such functions, based on the construction of conjugate harmonic pairs. Furthermore, if Ω is bounded with boundary Γ, where Γ is an Ahlfors-David regular surface, and if W is a ℝ0,m+1(r,p,q)-valued Hölder continuous function on Γ, then necessary and sufficient conditions are given under which W admits on Γ a Cauchy integral decomposition W=W++W−
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