arXiv subjects

Smiljana Jakšić

Publications and source records attributed to Smiljana Jakšić.

7 recordsLinked to original sources

arXiv2026

Continuity properties of the Laguerre operator and its propagator

We study the well-posedness of a Cauchy problem associated with the general form of the Laguerre operator and relate it to the corresponding global problem for the harmonic oscillator. To this end, we carry out a detailed analysis of the continuity properties of the associated propagator. Furthermore, we establish connections between several integral transforms, including the fractional Fourier transform and the fractional Hankel transform. Our results highlight the role of Pilipović spaces on positive orthants when studying problems involving the Laguerre operator.

math.AP↗

arXiv2025

Abelian and Tauberian results for the fractional Hankel transform in Zemanian-type spaces

In this paper, we first present an Abelian-type theorem for the fractional Hankel transform (FrHT) within Zemanian generalized function spaces. To prove this, we show that these spaces have the Montel property. Next, we construct a new Zemanian-type space as a projective limit of suitable Banach spaces. Its dual is the largest known distribution space admitting the FrHT. Finally, within this extended setting, we establish new Abelian and Tauberian-type results for the FrHT.

math.FA↗

arXiv2025

Abelian and Tauberian results for the fractional Hankel transform in Zemanian-type spaces

math.FA↗

arXiv2025

Abelian and Tauberian Results for the Fractional Hankel Transform of Generalized Functions

This paper aims to explore the quasiasymptotic behavior of distributions through the fractional Hankel transform. We present Tauberian result that connects the asymptotic behavior of generalized functions in the Zemanian space with the asymptotics of their fractional Hankel transform. Additionally, we establish both the initial and final value theorems for the fractional Hankel transform of distributions.

math.FA↗

arXiv2024

Ultradifferentiable functions via the Laguerre operator

We define and characterize ultradifferentiable functions and their corresponding ultradistributions on $\RR^d_+$ using iterates of the Laguerre operator. The characterization is based on decay or growth conditions of the coefficients in their Laguerre series expansion. We apply our results to establish an isomorphism between subspaces of Pilipović spaces on $\RR^d$, and the spaces of ultradifferentiable functions on $\RR^d_+$.

math.FA↗

arXiv2024

On the iterates of the Laguerre operator

We use the iterates of the Laguerre operator to introduce Pilipović spaces on positive orthants. It is shown that such spaces coincide with $G-$type spaces $g_α^α(\mathbb{R}^d_+)$ and $G_α^α(\mathbb{R}^d_+)$, when $α> 1$, and $α\geq 1$, respectively. However, in contrast to $G$-type spaces, Pilipović spaces on positive orthants are nontrivial below the critical index $α= 1$. We also remark that there is a natural isomorphism between subspaces of Pilipović spaces on $\mathbb{R}^d$ consisting of even functions, and Pilipović spaces on positive orthants.

math.FA↗

arXiv2022

The affine ensemble: determinantal point processes associated with the ax+b group

We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function ψ. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set Ω contained in C^+. As a special case one recovers the DPP related to the weighted Bergman kernel. When ψ is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.

math.PR↗