General Aspects of Jackson Calculus in Clifford Analysis

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
General Aspects of Jackson Calculus in Clifford Analysis
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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