scholarly journals The Radon transform between monogenic and generalized slice monogenic functions

2015 ◽  
Vol 363 (3-4) ◽  
pp. 733-752 ◽  
Author(s):  
F. Colombo ◽  
R. Lávička ◽  
I. Sabadini ◽  
V. Souček
Keyword(s):  
Radon Transform ◽  
Monogenic Functions ◽  
Slice Monogenic Functions

scholarly journals Distributions and the Global Operator of Slice Monogenic Functions

2013 ◽  
Vol 8 (6) ◽  
pp. 1257-1268 ◽  
Author(s):  
Fabrizio Colombo ◽  
Franciscus Sommen
Keyword(s):  
Monogenic Functions ◽  
Global Operator ◽  
Slice Monogenic Functions

scholarly journals A nonconstant coefficients differential operator associated to slice monogenic functions

2012 ◽  
Vol 365 (1) ◽  
pp. 303-318 ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini
Keyword(s):  
Differential Operator ◽  
Monogenic Functions ◽  
Slice Monogenic Functions

The Bergman-Sce transform for slice monogenic functions

2011 ◽  
Vol 34 (15) ◽  
pp. 1896-1909 ◽  
Author(s):  
Fabrizio Colombo ◽  
Jose O. Gonzàles Cervantes ◽  
Irene Sabadini
Keyword(s):  
Monogenic Functions ◽  
Slice Monogenic Functions

scholarly journals Bargmann–Radon transform for axially monogenic functions

2019 ◽  
Vol 65 (11) ◽  
pp. 1846-1861
Author(s):  
Alí Guzmán Adán ◽  
Ren Hu ◽  
Tim Raeymaekers ◽  
Franciscus Sommen
Keyword(s):  
Radon Transform ◽  
Monogenic Functions

Comparison of the Various Notions of Slice Monogenic Functions and Their Variations

2011 ◽  
Author(s):  
Fabrizio Colombo ◽  
J. Oscar González-Cervantes ◽  
Irene Sabadini ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Monogenic Functions ◽  
Slice Monogenic Functions

An extension theorem for slice monogenic functions and some of its consequences

2010 ◽  
Vol 177 (1) ◽  
pp. 369-389 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Daniele C. Struppa
Keyword(s):  
Extension Theorem ◽  
Monogenic Functions ◽  
Slice Monogenic Functions

Szegö–Radon Transform for Biaxially Monogenic Functions

2019 ◽  
Vol 29 (5) ◽  
Author(s):  
Ren Hu ◽  
Tim Raeymaekers ◽  
Franciscus Sommen
Keyword(s):  
Radon Transform ◽  
Monogenic Functions

The -spectrum and the -functional calculus

2012 ◽  
Vol 142 (3) ◽  
pp. 479-500 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Banach Space ◽  
Functional Calculus ◽  
Resolvent Operator ◽  
Monogenic Functions ◽  
Commuting Operators ◽  
Correct Definition ◽  
Slice Monogenic Functions ◽  
Definition Of ◽  
Integral Version

In some recent papers (called $\mathcal{S}$-functional calculus) for n-tuples of both bounded and unbounded not-necessarily commuting operators. The $\mathcal{S}$-functional calculus is based on the notion of $\mathcal{S}$-spectrum, which naturally arises from the definition of the $\mathcal{S}$-resolvent operator for n-tuples of operators. The $\mathcal{S}$-resolvent operator plays the same role as the usual resolvent operator for the Riesz–Dunford functional calculus, which is associated to a complex operator acting on a Banach space. When one considers commuting operators (bounded or unbounded) there is the possibility of simplifying the computation of the $\mathcal{S}$-spectrum. In fact, in this case we can use the F-spectrum, which is easier to compute than the $\mathcal{S}$-spectrum. In the case of commuting operators, our functional calculus is based on the $\mathcal{F}$-spectrum and will be called $\mathcal{SC}$-functional calculus. We point out that for a correct definition of the $\mathcal{S}$-resolvent operator and of the $\mathcal{SC}$-resolvent operator in the unbounded case we have to face different extension problems. Another reason for a more detailed study of the $\mathcal{F}$-spectrum is that it is related to the $\mathcal{F}$-functional calculus which is based on the integral version of the Fueter mapping theorem. This functional calculus is associated to monogenic functions constructed by starting from slice monogenic functions.

scholarly journals Slice monogenic functions of a Clifford variable via the 𝑆-functional calculus

2021 ◽  
Vol 8 (23) ◽  
pp. 281-296
Author(s):  
Fabrizio Colombo ◽  
David Kimsey ◽  
Stefano Pinton ◽  
Irene Sabadini
Keyword(s):  
Functional Calculus ◽  
Clifford Algebras ◽  
Function Theory ◽  
Monogenic Functions ◽  
Content Type ◽  
New Class ◽  
Zero Divisors ◽  
Slice Monogenic Functions ◽  
Class Of Functions ◽  
Clifford Numbers

In this paper we define a new function theory of slice monogenic functions of a Clifford variable using the S S -functional calculus for Clifford numbers. Previous attempts of such a function theory were obstructed by the fact that Clifford algebras, of sufficiently high order, have zero divisors. The fact that Clifford algebras have zero divisors does not pose any difficulty whatsoever with respect to our approach. The new class of functions introduced in this paper will be called the class of slice monogenic Clifford functions to stress the fact that they are defined on open sets of the Clifford algebra R n \mathbb {R}_n . The methodology can be generalized, for example, to handle the case of noncommuting matrix variables.

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