We propose a slightly modified definition for the Fourier-Mukai transform (on abelian varieties) that makes it much easier to remember various formulas. As an application, we give relatively short proofs two important theorems: characterization of GV-sheaves in terms vanishing, due Hacon; and fact M-regularity implies (continuous) global generation, Pareschi Popa.

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...

Nowadays, Radar systems have many applications and radar imaging is one of the most important of these applications. Inverse Synthetic Aperture Radar (ISAR) is used to form an image from moving targets. Conventional methods use Fourier transform to retrieve Doppler information. However, because of maneuvering of the target, the Doppler spectrum becomes time-varying and the image is blurred. Joi...

We propose an algorithm for recovering the matrix A in X = AS where X is a random vector of lower dimension than S. S is assumed to be sparse in the sense that S has less nonzero elements than the dimension of X at any given time instant. In contrast to previous approaches, the computational time of the presented algorithm is linear in the sample number and independent of source dimension, and ...

The 2-D Fourier transform has been generalized into the 2-D separable fractional Fourier transform (replaces 1-D Fourier transform by 1-D fractional Fourier transform for each variable) and the 2-D separable canonical transform (further replaces the fractional Fourier transform by canonical transform) in [3]. It also has been generalized into the 2-D unseparable fractional Fourier transform wit...