Snježana Maksimović

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

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

Asymptotic results for the distributional fractional Stockwell and fractional wavelet transforms

We provide some Abelian and Tauberian results characterizing the quasiasymptotic behavior of Lizorkin distributions in terms of their Stockwell transform. We prove the continuity of the fractional wavelet transform and the corresponding synthesis operator on the Schwartz spaces and their duals, respectively. Additionally, we establish a connection between fractional Stockwell and fractional wavelet transforms and provide some asymptotic results for the distributional fractional wavelet transform.

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↗

arXiv2020

Directional short-time Fourier transform of ultradistributions

We define and analyse the $k$-directional short-time Fourier transform and its synthesis operator over Gelfand Shilov spaces $\mathcal S^α_β(\mathbb R^n)$ and $\mathcal S^α_β(\mathbb R^{k+n})$ respectively, and their duals. Also, we investigate directional regular sets and their complements - directional wave fronts, for elements of $\mathcal S^{\prime α}_α(\mathbb R^n)$.

math.FA↗