The Radon transform between monogenic and generalized slice monogenic functions

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

The Radon transform between monogenic and generalized slice monogenic functions

Original language description

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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GBP201%2F12%2FG028" target="_blank" >GBP201/12/G028: Eduard Čech Institute for algebra, geometry and mathematical physics</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2015

Confidentiality

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

Name of the periodical

Mathematische Annalen

ISSN

0025-5831

e-ISSN

—

Volume of the periodical

363

Issue of the periodical within the volume

3-4

Country of publishing house

DE - GERMANY

Number of pages

20

Pages from-to

733-752

UT code for WoS article

000363037800002

EID of the result in the Scopus database

2-s2.0-84945462049