A new approach to Cullen-regular functions of a quaternionic variable

By Graziano Gentili, Daniele C. Struppa. 2006

235 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6fa4854851d802b4907c49ec1bd6058ef3a44d6c

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In Algebra and Number Theory

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Entire slice regular functions (2015, background): “The theory of slice regular functions was delevoped in the papers [47, 104, 106, 107, 109, 110, 112, 113], in particular, the zeros”
Continuous slice functional calculus in quaternionic Hilbert spaces (2012, background): “The concept of slice regularity for functions of one quaternionic variable has been introduced by Gentili and Struppa in [15, 16] and then extended to octonions, Clifford algebras and in general real alternative –algebras in [7, 17, 19, 20].”
On the Multiplicity of Zeroes of Polynomials with Quaternionic Coefficients (2008, background): “real quaternion q can be written in au nique way asq = x + yI, with I ∈ S and x, y ∈ R ,y > 0. We will refer to x = Re(q) as the real part of q and y = Im(q) as the imaginary part of q. Quite recently, [ 2 ], [3], we developed a new theory of regularity for functions of a quaternionic variable.”
Regular Functions on the Space of Cayley Numbers (2010, background): “A description of this theory can be found in [ 11 ], [12], but the interested reader can find the most recent developments in [10] and [3].”
The open mapping theorem for regular quaternionic functions (2008, background): “The proofs involve some peculiar geometric properties of such functions which are of independent interest.”
Quaternionic-valued ordinary differential equations. The Riccati equation (2009, unknown): “[9, 8]) but the quaternionic version of the Wolff–Denjoy theorem has not been obtained yet.”
Global differential equations for slice regular functions (2014, methodology): “It was introduced firstly for functions of one quaternionic variable by Gentili and Struppa in [4], [5], and then extended to octonionic variable in [6].”
Non Commutative Functional Calculus: Bounded Operators (2007, background): “The key observation which allowed the study of such an eigenvalue problem, was the recent development of slice regular functions, [2,3].”
Regular Functions of a Quaternionic Variable (2013, methodology): “Chapter 1 explains in detail the definition of regularity given by Gentili and Struppa in [29, 30].”
Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, background): “Some references for this theory of functions are [33,38,56,57].”
A Cauchy kernel for slice regular functions (2009, methodology): “In recent papers, adopting an approach used by Cullen, the authors introduced a new theory of regular functions for quaternionic and Clifford valued functions, [3], [4], [11], [12], [13].”
Regular Moebius transformations of the space of quaternions (2008, background): “The theory presented in [13, 14] is based on the following definition of regularity for quaternionic functions (inspired by C.”
A New Theory of Regular Functions of a Quaternionic Variable (2007, methodology): “Finally, we conclude with a simple and nice result which we had originally announced in [6] Proposition 5.”
Slice monogenic functions (2007, methodology): “Recently, Gentili and Struppa adopted a definition of regularity (slice regularity), see [6], [7], where they prove that slice regular functions can be expanded into power series ∑ n q an, with coefficients an ∈ H.”
The algebra of slice functions (2015, background): “In [11, 12], the authors constructed a class of quaternionic functions that includes the ring of polynomials just described (with R = H).”
Zeros of regular functions and polynomials of a quaternionic variable (2008, methodology): “It naturally leads to the formulation of an identity principle that generalizes the one stated in [6; 7].”
Slice regular functions on real alternative algebras (2010, background): “Proposition 8 implies that if A is the algebra of quaternions or octonions, and the domain D intersects the real axis, then f is slice regular on ΩD if and only if it is Cullen regular in the sense introduced by Gentili and Struppa in [18, 19] for quaternionic functions and in [22, 17] for octonioni”