O_α-transformation and its uncertainty principles

2025/03/19 by Minh, Lai Tien, Tuan, Trinh
#26D10 #42A38 #43A32 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.15132

Abstract

In this paper, we introduce a family of O_α-transformation based on kernels fusion of the fractional Fourier transform (abbreviated as FRFT) with angle α∉ πℤ. We point out this is a valid integral transform via establishing its basic operational properties. Besides, we survey various mathematical aspects of the uncertainty principles for the O_α-transform, including Heisenberg's inequality, logarithmic uncertainty inequality, local uncertainty inequality, Hardy's inequality, and Beurling-Hörmander's theorem.

Related

• The uncertainty principle: variations on a theme
• A mathematical survey on Fourier type integral transform and their offshoots: windowed Fourier transform, wavelet transform and Stockwell transform
• Heisenberg-Pauli-Weyl uncertainty principles for the fractional Dunkl transform on the real line
• Weighted inequalities and uncertainty principles for the \boldsymbol(k,a)-generalized Fourier transform
• N-dimensional Heisenberg's uncertainty principle for fractional Fourier transform