This monograph presents the summability of higher dimensional Fourier
series, and generalizes the concept of Lebesgue points. Focusing on
Fejér and Cesàro summability, as well as theta-summation, readers will
become more familiar with a wide variety of summability methods. Within
the theory of higher dimensional summability of Fourier series, the book
also provides a much-needed simple proof of Lebesgue's theorem, filling
a gap in the literature. Recent results and real-world applications are
highlighted as well, making this a timely resource.
The book is structured into four chapters, prioritizing clarity
throughout. Chapter One covers basic results from the one-dimensional
Fourier series, and offers a clear proof of the Lebesgue theorem. In
Chapter Two, convergence and boundedness results for the
lq-summability are presented. The restricted and
unrestricted rectangular summability are provided in Chapter Three, as
well as the sufficient and necessary condition for the norm convergence
of the rectangular theta-means. Chapter Four then introduces six types
of Lebesgue points for higher dimensional functions.
Lebesgue Points and Summability of Higher Dimensional Fourier Series
will appeal to researchers working in mathematical analysis,
particularly those interested in Fourier and harmonic analysis.
Researchers in applied fields will also find this useful.
