Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra
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2026
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| author | Lankpetre, Kawèyim Aremua, Isiaka Kyemba, Joseph Désiré Bukweli |
| author_facet | Lankpetre, Kawèyim Aremua, Isiaka Kyemba, Joseph Désiré Bukweli |
| contents | The purpose of this article is to develop and analyze $\mathcal{R}(p,q)-$topological analysis of the classical nuclear space within the general framework of $\mathcal{R}(p,q)-$calculus. We begin by introducing the $\mathcal{R}(p,q)-$Gamma functions, establishing their main properties and their connection with the deformed factorials. We develop a rigorous analytic and functional-analytic framework for holomorphic functions governed by a general $\mathcal{R}(p,q)-$deformation, where $\mathcal{R}(u,v)$ is a meromorphic kernel satisfying $0<q<p\leq 1$, $\mathcal{R}(1,1)=0$, and $\mathcal{R}(p^n,q^n)>0$.
A Stirling-type asymptotic expansion is established for the $\mathcal{R}(p,q)-$deformed Gamma function $Γ_{\mathcal{R}(p,q)}$, yielding precise exponential quadratic growth estimates driven by the asymptotics of the deformed factorial $\mathcal{R}!(p^n,q^n)\sim \exp(λn^2)$.
These asymptotics induce sharp coefficient bounds and Cauchy-type inequalities for $\mathcal{R}(p,q)-$entire functions. Based on these estimates, we introduce $\mathcal{R}(p,q)-$weighted Banach and Fréchet spaces of holomorphic functions, together with deformation dependent pseudo-norms and valuation maps.
Within this setting, we define $\mathcal{R}(p,q)-$discs and anisotropic sectors adapted to the deformation geometry and prove $\mathcal{R}(p,q)-$analogues of the Cauchy-Hadamard theorem, the Borel-Carathéodory inequality and Phragmén-Lindelöf type growth principles. These results contribute to the broader program of constructing a consistent functional calculus in $\mathcal{R}(p,q)-$quantum algebras, with potential applications to deformed fractional differential equations, operator theory, spectral problems, and non commutative models arising in mathematical physics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_24010 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra Lankpetre, Kawèyim Aremua, Isiaka Kyemba, Joseph Désiré Bukweli Quantum Algebra Mathematical Physics Functional Analysis 33E12, 33D90, 33B15, 33E20, 26A33, 81R50, 17B37 The purpose of this article is to develop and analyze $\mathcal{R}(p,q)-$topological analysis of the classical nuclear space within the general framework of $\mathcal{R}(p,q)-$calculus. We begin by introducing the $\mathcal{R}(p,q)-$Gamma functions, establishing their main properties and their connection with the deformed factorials. We develop a rigorous analytic and functional-analytic framework for holomorphic functions governed by a general $\mathcal{R}(p,q)-$deformation, where $\mathcal{R}(u,v)$ is a meromorphic kernel satisfying $0<q<p\leq 1$, $\mathcal{R}(1,1)=0$, and $\mathcal{R}(p^n,q^n)>0$. A Stirling-type asymptotic expansion is established for the $\mathcal{R}(p,q)-$deformed Gamma function $Γ_{\mathcal{R}(p,q)}$, yielding precise exponential quadratic growth estimates driven by the asymptotics of the deformed factorial $\mathcal{R}!(p^n,q^n)\sim \exp(λn^2)$. These asymptotics induce sharp coefficient bounds and Cauchy-type inequalities for $\mathcal{R}(p,q)-$entire functions. Based on these estimates, we introduce $\mathcal{R}(p,q)-$weighted Banach and Fréchet spaces of holomorphic functions, together with deformation dependent pseudo-norms and valuation maps. Within this setting, we define $\mathcal{R}(p,q)-$discs and anisotropic sectors adapted to the deformation geometry and prove $\mathcal{R}(p,q)-$analogues of the Cauchy-Hadamard theorem, the Borel-Carathéodory inequality and Phragmén-Lindelöf type growth principles. These results contribute to the broader program of constructing a consistent functional calculus in $\mathcal{R}(p,q)-$quantum algebras, with potential applications to deformed fractional differential equations, operator theory, spectral problems, and non commutative models arising in mathematical physics. |
| title | Topological analysis in $\mathcal{R}(p,q)-$anisotropic sector and nuclear space on $\mathcal{R}(p,q)-$quantum deformed algebra |
| topic | Quantum Algebra Mathematical Physics Functional Analysis 33E12, 33D90, 33B15, 33E20, 26A33, 81R50, 17B37 |
| url | https://arxiv.org/abs/2605.24010 |