منابع مشابه
Poles of regular quaternionic functions
This paper studies the singularities of Cullen-regular functions of one quaternionic variable, as defined in [7]. The quaternionic Laurent series prove to be Cullen-regular. The singularities of Cullenregular functions are thus classified as removable, essential or poles. The quaternionic analogues of meromorphic complex functions, called semiregular functions, turn out to be quotients of Culle...
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In this paper we prove a new representation formula for slice regular functions, which shows that the value of a slice regular function f at a point q = x + yI can be recovered by the values of f at the points q + yJ and q + yK for any choice of imaginary units I, J,K. This result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a...
متن کاملThe open mapping theorem for regular quaternionic functions
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular functions. The proofs involve some peculiar geometric properties of such functions which are of independent interest.
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For a polynomial ring, R, in 4n variables over a field, we consider the submodule of R corresponding to the 4 × 4n matrix made up of n groupings of the linear representation of quarternions with variable entries (which corresponds to the Cauchy-Fueter operator in partial differential equations) and let Mn be the corresponding quotient module. We compute many homological properties of Mn includi...
متن کاملQuaternionic linear algebra and plurisubharmonic functions of quaternionic variables
Quaternionic linear algebra and plurisubharmonic functions of quaternionic variables. Abstract We remind known and establish new properties of the Dieudonné and Moore determinants of quaternionic matrices. Using these linear algebraic results we develop a basic theory of plurisubharmonic functions of quaternionic variables. The main point of this paper is that in quaternionic algebra and analys...
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ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2009
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476930903275938