Resumen de Interpolation theory for the HK-Fourier transform

Juan H. Arredondo, Alfredo Reyes

• We use the Henstock–Kurzweil integral and interpolation theory to extend the Fourier cosine transform operator, broadening some classical properties such as the Riemann–Lebesgue lemma. Furthermore, we show that a qualitative difference between the cosine and sine transform is preserved on differentiable functions.