Directional short-time Fourier transform of ultradistributions

2020/10/20 by Atanasova, Sanja, Maksimović, Snježana, Pilipović, Stevan
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2010.10188

Abstract

We define and analyse the k-directional short-time Fourier transform and its synthesis operator over Gelfand Shilov spaces \mathcal S^α_β(\mathbb Rⁿ) 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^{′ α}_α(\mathbb Rⁿ).

Related

• Directional short-time Fourier transform and directional regularity
• Microlocal analysis for Gelfand--Shilov spaces
• Wave front sets with respect to Banach spaces of ultradistributions.\n Characterisation via the short-time Fourier transform
• The directional short-time fractional Fourier transform of distributions
• Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions