Macroeconomics

Quantum mechanics

Multiplier (economics)

Approx

Algorithm

Pointwise convergence

Applied mathematics

Operating system

Economics

Computer science

Fractional Fourier transform

Laser

Physics

Mathematics

Optics

Pointwise

Fourier analysis

Mathematical analysis

Gauss

Artificial neural network

Fourier transform

Machine learning

Chirp

Convolution (computer science)

Applied and Computational Harmonic Analysis

This paper is devoted to the Lp(R) theory of the fractional Fourier transform (FRFT) for 1≤p<2. In view of the special structure of the FRFT, we study FRFT properties of L1 functions, via the introduction of a suitable chirp operator. However, in the L1(R) setting, problems of convergence arise even when basic manipulations of functions are performed. We overcome such issues and study the FRFT inversion problem via approximation by suitable means, such as the fractional Gauss and Abel means. We also obtain the regularity of fractional convolution and results on pointwise convergence of FRFT means. Finally we discuss Lp multiplier results and a Littlewood-Paley theorem associated with FRFT.

Fractional Fourier transforms on L and applications