منابع مشابه
Slice monogenic functions
In this paper we offer a new definition of monogenicity for functions defined on R with values in the Clifford algebra Rn following an idea inspired by the recent papers [6], [7]. This new class of monogenic functions contains the polynomials (and, more in general, power series) with coefficients in the Clifford algebra Rn. We will prove a Cauchy integral formula as well as some of its conseque...
متن کاملFinely Differentiable Monogenic Functions
Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in [12] like a higher dimensional analogue of finely holomorphic functions.
متن کاملMonogenic Functions in Conformal Geometry⋆
Monogenic functions are basic to Clifford analysis. On Euclidean space they are defined as smooth functions with values in the corresponding Clifford algebra satisfying a certain system of first order differential equations, usually referred to as the Dirac equation. There are two equally natural extensions of these equations to a Riemannian spin manifold only one of which is conformally invari...
متن کاملThe Runge Theorem for Slice Hyperholomorphic Functions
In this paper we introduce and study rational slice monogenic functions. After proving a decomposition theorem for such functions, we are able to prove the Runge approximation theorem for slice monogenic functions. We then show how a similar argument can be used to obtain an analogue of the Runge approximation theorem in the slice regular setting.
متن کاملA Cauchy kernel for slice regular functions
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the expression of the derivatives of a regular function in terms of the powers of the Cauchy kernel, and we present several other consequent results. AMS Classific...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2009
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-009-0055-4