Interpolation theory for the HK-Fourier transform

• Juan H. Arredondo ^[1] ; Alfredo Reyes ^[1]
  1. [1] Universidad Autónoma Metropolitana

     Universidad Autónoma Metropolitana

     México

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 62, Nº. 2, 2021, págs. 401-413
• Idioma: inglés
• DOI: 10.33044/revuma.1911
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• Resumen

  • 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.