Steps of the proof 1. Calculation of Fourier coefficients $$ { \hat {\Delta}_a (n) }$$ and confirmation of the sign First, to confirm the hint " $$ { \hat {\Delta}_a (n) \ge 0 }$$ ", we calculate the ...

A differentiable fractional Fourier transform (FRFT) implementation with layers that can be trained end-to-end with the rest of the network. This package provides implementations of both fast ...

Abstract: Convolution is fundamental in digital signal processing across many applications. Existing works enable N-point linear convolution via N-point right-angle circular convolution (RCC) based on ...

Quantum Fourier analysis is a powerful tool in mathematical physics. Here, we introduce quantum, higher-order Fourier analysis (q-HOFA). We explore some mathematical properties of this theory and show ...

Our research proves a conjecture from string theory asserting the vanishing of a specific convolution sum arising in the 4-graviton scattering amplitude in 10-dimensional type IIB string theory. The ...

This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is ...

Department of Chemistry, UCL (University College London), 20 Gordon Street, London WC1H 0AJ, U.K. Department of Chemistry, Institute of Environmental Studies and Natural Resources (i-UNAT, FEAM), ...

The Fourier Neural Operator (FNO) [1] is a neural operator with an integral kernel parameterized in Fourier space. This allows for an expressive and efficient architecture. Applications of the FNO ...

Physics-informed convolutional recurrent network (PhyCRNet) can solve partial differential equations without labeled data by encoding physics constraints into the loss function. However, the ...