A Structure Formula for Slice Monogenic Functions and Some of its Consequences

By Fabrizio Colombo, Irene Sabadini. 2008

78 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/89350ec1f12684f7d7a88fce3f906bb5b0de51d7

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In Algebra and Number Theory

In Applied Mathematics

Citations in the corpus

On Two Approaches to the Bergman Theory for Slice Regular Functions (2013, methodology): “Slice regular functions obey the following property (see [5, 9]).”
Pontryagin-de Branges-Rovnyak spaces of slice hyperholomorphic functions (2012, unknown): “Slice hyperholomorphic functions have two main formulations according to the fact that the functions we consider are defined on quaternions and are quaternion-valued, in this case the functions are called slice regular, see [32, 15, 19] or the functions are defined on the Euclidean space R and have ”
The C-property for slice regular functions and applications to the Bergman space (2013, background): “The Representation Formula shows that all the slice regular functions defined on axially symmetric s-domains are of the form (see [7]) f(q) = f(x+ Iqy) = α(x, y) + Iqβ(x, y) (6) where α, β are H-valued, such that α(x,−y) = α(x, y), β(x,−y) = −β(x, y) (7) and they satisfying the Cauchy-Riemann system”
The $H^\infty$ functional calculus based on the $S$-spectrum for quaternionic operators and for $n$-tuples of noncommuting operators (2015, unknown): “The crucial result of slice hyperholomorphic functions is the representation formula (or structure formula), first proved in [16].”
The Fueter mapping theorem in integral form and the ℱ‐functional calculus (2010, methodology): “12 (Structure Formula, see [4]) Let U⊆Rn+1 be an axially symmetric s-domain and let f be an s-monogenic function on U.”
An extension theorem for slice monogenic functions and some of its consequences (2010, methodology): “Representation and extension properties of slice monogenic functions In this section we begin with a very important representation formula which first appeared in [2], and we will then use it to prove the extension result mentioned in the introduction.”
Schur Functions and Their Realizations in the Slice Hyperholomorphic Setting (2011, background): “Some references for this theory of functions are [56, 33, 38].”
On Some Properties of the Quaternionic Functional Calculus (2009, background): “Such a theory is a natural tool to define a functional calculus for n-tuples of noncommuting operators, see [8] and [2, 3].”
Entire slice regular functions (2015, methodology): “The theory of slice regular functions started in [109] and [110] for functions defined at ball centered at the origin and then evolved in a series of papers, among which we mention [58], [46], [47], into a theory on axially symmetric domains.”
Slice regular functions on real alternative algebras (2010, methodology): “We define a Cauchy kernel, which in the quaternionic case was already introduced in [3], and for slice monogenic functions in [5, 6].”