Slice Hyperholomorphic Functions

2020 ◽  
pp. 23-39
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions

scholarly journals BMO- and VMO-spaces of slice hyperholomorphic functions

2017 ◽  
Vol 290 (14-15) ◽  
pp. 2259-2279
Author(s):  
Jonathan Gantner ◽  
J. Oscar González-Cervantes ◽  
Tim Janssens
Keyword(s):  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions

Interpolation Problems for Certain Classes of Slice Hyperholomorphic Functions

2016 ◽  
Vol 86 (2) ◽  
pp. 165-183 ◽  
Author(s):  
Daniel Alpay ◽  
Vladimir Bolotnikov ◽  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Slice Hyperholomorphic Functions ◽  
Interpolation Problems ◽  
Hyperholomorphic Functions

scholarly journals The Pompeiu formula for slice hyperholomorphic functions

2011 ◽  
Vol 60 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Fabrizio Colombo ◽  
Irene Sabadini ◽  
Daniel Struppa
Keyword(s):  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions

Some Integral Representations of Slice Hyperholomorphic Functions

2014 ◽  
Vol 14 (3) ◽  
pp. 473-489 ◽  
Author(s):  
F. Colombo ◽  
J. O. González-Cervantes ◽  
I. Sabadini
Keyword(s):  
Integral Representations ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions

scholarly journals Bloch, Besov and Dirichlet Spaces of Slice Hyperholomorphic Functions

2014 ◽  
Vol 9 (2) ◽  
pp. 479-517 ◽  
Author(s):  
C. Marco Polo Castillo Villalba ◽  
Fabrizio Colombo ◽  
Jonathan Gantner ◽  
J. Oscar González-Cervantes
Keyword(s):  
Dirichlet Spaces ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions

scholarly journals An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators

2021 ◽  
Vol 31 (3) ◽  
Author(s):  
Fabrizio Colombo ◽  
Jonathan Gantner ◽  
Stefano Pinton
Keyword(s):  
Spectral Theory ◽  
Functional Calculus ◽  
Natural Extension ◽  
Several Complex Variables ◽  
Monogenic Functions ◽  
Fractional Powers ◽  
Holomorphic Functional Calculus ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions ◽  
Nonhomogeneous Materials

AbstractThe aim of this paper is to give an overview of the spectral theories associated with the notions of holomorphicity in dimension greater than one. A first natural extension is the theory of several complex variables whose Cauchy formula is used to define the holomorphic functional calculus for n-tuples of operators $$(A_1,\ldots ,A_n)$$ ( A 1 , … , A n ) . A second way is to consider hyperholomorphic functions of quaternionic or paravector variables. In this case, by the Fueter-Sce-Qian mapping theorem, we have two different notions of hyperholomorphic functions that are called slice hyperholomorphic functions and monogenic functions. Slice hyperholomorphic functions generate the spectral theory based on the S-spectrum while monogenic functions induce the spectral theory based on the monogenic spectrum. There is also an interesting relation between the two hyperholomorphic spectral theories via the F-functional calculus. The two hyperholomorphic spectral theories have different and complementary applications. We finally discuss how to define the fractional Fourier’s law for nonhomogeneous materials using the spectral theory on the S-spectrum.

scholarly journals Realizations of holomorphic and slice hyperholomorphic functions: The Krein space case

2020 ◽  
Vol 31 (4) ◽  
pp. 607-628
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Irene Sabadini
Keyword(s):  
Krein Space ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions ◽  
Kreĭn Space ◽  
Space Case

scholarly journals Positive and Generalized Positive Real Lemma for Slice Hyperholomorphic Functions

2019 ◽  
Vol 91 (1) ◽  
Author(s):  
Daniel Alpay ◽  
Fabrizio Colombo ◽  
Izchak Lewkowicz ◽  
Irene Sabadini
Keyword(s):  
Positive Real ◽  
Slice Hyperholomorphic Functions ◽  
Hyperholomorphic Functions
Sign in / Sign up

Export Citation Format

Share Document