Springer Trigonometric Fourier Series and Their Conjugates: 372 (Mathematics and Its Applications, 372)

Product Description This book presents in a coherent way the results obtained in the following aspects of the theory of multiple trigonometric Fourier series: the existence and properties of the conjugates and Hilbert transforms of integrable functions of several variables; convergence of Fourier series and their conjugates, as well as their summability by Cesàro and Abel-Poisson methods; and approximating properties of Cesàro means of Fourier series and their conjugates. Special emphasis is put on new effects which arise from dealing with multiple series and which are not inherent in the one-dimensional case. Unsolved problems are formulated separately. Audience: This volume will prove useful to both graduate students and research workers in the field of Fourier analysis, approximations and expansions, integral transforms, and operational calculus. Review ` ... wealth of material collected ... We recommend it to everyone who wants to get fresh information on recent results in a very traditional part of Fourier analysis. ' Mathematical Reviews Clippings 97k