Features and technical details
This book investigates the convergence and summability of both one-dimensional and multi-dimensional Fourier transforms, as well as the theory of Hardy spaces. To do so, it studies a general summability method known as theta-summation, which encompasses all the well-known summability methods, such as the FejÃ©r, Riesz, Weierstrass, Abel, Picard, Bessel and Rogosinski summations.Â Following on the classic books by Bary (1964) and Zygmund (1968), this is the first book that considers strong summability introduced by current methodology. A further unique aspect is that the Lebesgue points are also studied in the theory of multi-dimensional summability. In addition to classical results, results from the past 20-30 years â normally only found in scattered research papers â are also gathered and discussed, offering readers a convenient âone-stopâ source to support their work. As such, the book will be useful for researchers, graduate and postgraduate students alike.