The Radon transform between monogenic and generalized slice monogenic functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F15%3A10317154" target="_blank" >RIV/00216208:11320/15:10317154 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/s00208-015-1182-3" target="_blank" >http://dx.doi.org/10.1007/s00208-015-1182-3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-015-1182-3" target="_blank" >10.1007/s00208-015-1182-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Radon transform between monogenic and generalized slice monogenic functions

Popis výsledku v původním jazyce

In Bures et al. (Elements of quaternionic analysis and Radon transform, 2009), the authors describe a link between holomorphic functions depending on a parameter and monogenic functions defined on using the Radon and dual Radon transforms. The main aim of this paper is to further develop this approach. In fact, the Radon transform for functions with values in the Clifford algebra is mapping solutions of the generalized Cauchy-Riemann equation, i.e., monogenic functions, to a parametric family of holomorphic functions with values in and, analogously, the dual Radon transform is mapping parametric families of holomorphic functions as above to monogenic functions. The parametric families of holomorphic functions considered in the paper can be viewed as ageneralization of the so-called slice monogenic functions. An important part of the problem solved in the paper is to find a suitable definition of the function spaces serving as the domain and the target of both integral transforms.

Název v anglickém jazyce

The Radon transform between monogenic and generalized slice monogenic functions

Popis výsledku anglicky

In Bures et al. (Elements of quaternionic analysis and Radon transform, 2009), the authors describe a link between holomorphic functions depending on a parameter and monogenic functions defined on using the Radon and dual Radon transforms. The main aim of this paper is to further develop this approach. In fact, the Radon transform for functions with values in the Clifford algebra is mapping solutions of the generalized Cauchy-Riemann equation, i.e., monogenic functions, to a parametric family of holomorphic functions with values in and, analogously, the dual Radon transform is mapping parametric families of holomorphic functions as above to monogenic functions. The parametric families of holomorphic functions considered in the paper can be viewed as ageneralization of the so-called slice monogenic functions. An important part of the problem solved in the paper is to find a suitable definition of the function spaces serving as the domain and the target of both integral transforms.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Ústav Eduarda Čecha pro algebru, geometrii a matematickou fyziku</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2015

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

—

Svazek periodika

363

Číslo periodika v rámci svazku

3-4

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

20

Strana od-do

733-752

Kód UT WoS článku

000363037800002

EID výsledku v databázi Scopus

2-s2.0-84945462049