Interpolation theory for the HK-Fourier Transform

Ponente(s): Alfredo Reyes Vazquez

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.