Orthogonal Series (Translations of Mathematical Monographs)

Explore the foundational principles of mathematical analysis with Orthogonal Series, part of the Translations of Mathematical Monographs series. This text traces the evolution of general orthogonal series from their origins at the turn of the century, rooted in the generalization of trigonometric series through Lebesgue integration. While the theory began long ago, recent developments over the last 25 years have transformed the field. Researchers have discovered that many properties once thought unique to trigonometric systems actually apply to a much wider class of orthonormal systems. This book provides a deep study of these fundamental methods, making it a necessary resource for those studying advanced mathematical theory. By focusing on general orthonormal systems and specific examples like the Haar and Franklin systems, this volume serves as a comprehensive guide for academics and students in the mathematical sciences. It offers a clear look at how modern developments have expanded our understanding of orthonormal systems beyond traditional trigonometric models.