General Aspects of Jackson Calculus in Clifford Analysis

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F25%3AA26039ZH" target="_blank" >RIV/61988987:17310/25:A26039ZH - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00006-025-01374-x#citeas" target="_blank" >https://link.springer.com/article/10.1007/s00006-025-01374-x#citeas</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00006-025-01374-x" target="_blank" >10.1007/s00006-025-01374-x</a>

Jazyk výsledku

angličtina

Název v původním jazyce

General Aspects of Jackson Calculus in Clifford Analysis

Popis výsledku v původním jazyce

We consider an extension of Jackson calculus into higher dimensions and specifically into Clifford analysis for the case of commuting variables. In this case, Dirac is the operator of the first $q$-partial derivatives (or $q$-differences) ${}_qD = sum_{I=1}^n e_i {}_q{partial}_i$, where ${}_q {partial_i} denotes the $q$-partial derivative with respect to $x_i$. This Dirac operator factorizes the $q$-deformed Laplace operator. Similar to the case of classical Clifford analysis, we then consider the $q$-deformed Euler and Gamma operators and their relations to each other. Nullsolutions of this $q$-Dirac equation are called $q$-monogenic. Using the Fischer decomposition, we can decompose the space of homogeneous polynomials into spaces of $q$-monogenic polynomials. Using the $q$-deformed Cauchy-Kovalevskaya extension theorem, we can construct $q$-monogenic functions. Overall, we show the analogies and the differences between classical Clifford and Jackson-Clifford analysis. In particular, $q$-monogenic functions need not be monogenic and vice versa.

Název v anglickém jazyce

General Aspects of Jackson Calculus in Clifford Analysis

Popis výsledku anglicky

We consider an extension of Jackson calculus into higher dimensions and specifically into Clifford analysis for the case of commuting variables. In this case, Dirac is the operator of the first $q$-partial derivatives (or $q$-differences) ${}_qD = sum_{I=1}^n e_i {}_q{partial}_i$, where ${}_q {partial_i} denotes the $q$-partial derivative with respect to $x_i$. This Dirac operator factorizes the $q$-deformed Laplace operator. Similar to the case of classical Clifford analysis, we then consider the $q$-deformed Euler and Gamma operators and their relations to each other. Nullsolutions of this $q$-Dirac equation are called $q$-monogenic. Using the Fischer decomposition, we can decompose the space of homogeneous polynomials into spaces of $q$-monogenic polynomials. Using the $q$-deformed Cauchy-Kovalevskaya extension theorem, we can construct $q$-monogenic functions. Overall, we show the analogies and the differences between classical Clifford and Jackson-Clifford analysis. In particular, $q$-monogenic functions need not be monogenic and vice versa.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

ADV APPL CLIFFORD AL

ISSN

0188-7009

e-ISSN

1661-4909

Svazek periodika

—

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

18

Strana od-do

—

Kód UT WoS článku

001429170700001

EID výsledku v databázi Scopus

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