Noncommutative Functional Calculus

Colombo, Fabrizio; Sabadini, Irene; Struppa, Daniele C.

doi:10.1007/978-3-0348-0110-2

Cited by 269 publications

(138 citation statements)

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“…Note that such a function f is slice monogenic in the sense of [7], (for more detail on slice monogenic functions and some of their applications see [2], [3], [5], [8], [9], [10], [11]). In the recent paper [6] we have proved an integral representation formula for f (x 0 , ρ) in terms of the functionf (x 0 , ρ), wheref (x 0 , ρ) and f (x 0 , ρ) are related by…”

Section: Introduction and Notationsmentioning

confidence: 99%

The inverse Fueter mapping theorem in integral form using spherical monogenics

2012

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In this paper we prove an integral representation formula for the inverse Fueter mapping theorem for monogenic functions defined on axially symmetric open sets U ⊆ R n+1 , i.e. on open sets U invariant under the action of SO(n). Every monogenic function on such an open set U can be written as a series of axially monogenic functions of degree k, i.e. functions of typef k (x) := [A(x 0 , ρ) + ωB(x 0 , ρ)]P k (ω), where A(x 0 , ρ) and B(x 0 , ρ) satisfy a suitable Vekua-type system and P k (ω) are spherical monogenic polynomials of degree k. The Fueter mapping theorem says that given a holomorphic function f of a paravector variable defined on U then the functionf (x)P k (x) given byis a monogenic function. The aim of this paper is to invert the Fueter mapping theorem by determining a holomorphic function f of a paravector variable in terms off (x)P k (x). This result allows to invert the Fueter mapping theorem for any monogenic function defined on an axially symmetric open set.

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Section: Introduction and Notationsmentioning

confidence: 99%

The inverse Fueter mapping theorem in integral form using spherical monogenics

2012

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“…The influence of Heinz is also profound in the second direction of research taken in the last years by the first editor with Fabrizio Colombo and Irene Sabadini from Politecnico di Milano, where in particular Schur analysis is considered in the setting of slice hyperholomorphic functions (see [13] for the latter) and quaternionic Pontryagin spaces. The paper [6] extends the Krein-Langer factorization of generalized Schur functions.…”

Section: Telle Est La Morale Que Mermoz Et D'autres Nous Ont Enseignémentioning

confidence: 99%

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

Sakhnovich¹

2018

Operator Theory: Advances and Applications

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“…Quaternionic analysis is an active area of current research (see, for example, [5,6,10,12] and references cited therein). Here we shall be using Hilbert spaces over the quaternions and some elements of group representation theory on them.…”

Section: Some Quaternionic Factsmentioning

confidence: 99%

On Some Quaternionic Coherent States and Wavelets

Ali

2015

Trends in Mathematics

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As a natural extension of the affine groups of the reals and the complexes, leading to one and two-dimensional wavelets, we look at the quaternionic affine group and its representations on both complex and quaternionic Hilbert spaces. We then study the problem of coherent states and wavelets built from these representations.Mathematics Subject Classification (2010). Primary 81R30; Secondary 57S20.

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Noncommutative Functional Calculus

Cited by 269 publications

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The inverse Fueter mapping theorem in integral form using spherical monogenics

The inverse Fueter mapping theorem in integral form using spherical monogenics

Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations

On Some Quaternionic Coherent States and Wavelets

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