منابع مشابه
A 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...
متن کاملExtension results for slice regular functions of a quaternionic variable
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...
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The celebrated 100-year old Phragmén-Lindelöf theorem, [15, 16], is a far reaching extension of the maximum modulus theorem for holomorphic functions that in its simplest form can be stated as follows: Theorem 1.1. Let Ω ⊂ C be a simply connected domain whose boundary contains the point at infinity. If f is a bounded holomorphic function on Ω and lim supz→z0 |f(z)| ≤ M at each finite boundary p...
متن کاملThe zero sets of slice regular functions and the open mapping theorem
A new class of regular quaternionic functions, defined by power series in a natural fashion, has been introduced in [11]. Several results of the theory recall the classical complex analysis, whereas other results reflect the peculiarity of the quaternionic structure. The recent [1] identified a larger class of domains, on which the study of regular functions is most natural and not limited to t...
متن کاملSlice 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...
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ژورنال
عنوان ژورنال: The Journal of Geometric Analysis
سال: 2020
ISSN: 1050-6926,1559-002X
DOI: 10.1007/s12220-020-00551-7