Modern Problems of Mathematics of Mechanics . T. 10. Mathematics. Issue. 1. On the 60th anniversary of the workshop: Trigonometric and orthogonal series" , Created by a team of authors, It is an important scientific publication ,. which will be a valuable resource for professional mathematicians, Researchers in Theoretical Mechanics and Students , seeking to deepen their knowledge in the field of modern mathematical methods. This book is part of a series devoted to topical issues of mathematics and mechanics, and is particularly notable for its scientific approach, wealth of theoretical developments and practical applications. This publication is devoted to one of the key topics of modern mathematics - trigonometric and orthogonal series. In it, the authors consider not only the classical methods of decomposition of functions into series, but also explore new approaches relevant in the context of modern problems of mechanics and physics. Particular attention is paid to convergence, spectral characteristics and the use of orthogonal systems in solving differential equations, which makes the book especially valuable for those who are engaged in mathematical modeling and numerical methods. Modern Problems of Mathematics of Mechanics . T. 10. Mathematics. Issue. 1. For the 60th anniversary of the seminar" is intended for scientists, graduate students and senior students who are looking for a deep understanding of the mathematical foundations of mechanics and modern methods of analysis. It will be of interest to specialists working in the field of mathematical physics, function theory and numerical methods, as well as teachers seeking to expand their knowledge and prepare students for solving complex scientific problems. Age range of readers - from master's students to experienced researchers who want to stay up to date with the latest achievements in the field of trigonometric and orthogonal decompositions. The peculiarity of this book is not only theoretical analysis, but also practical orientation. It deals in detail with the application of trigonometric and orthogonal series in solving problems of mechanics, hydrodynamics, electromagnetism and other areas of physics. The author's team, which unites leading scientists, uses a clear and accessible style of presentation, which makes complex mathematical concepts more understandable and fascinating. The book traces the connection between classical methods and modern directions of research, which allows the reader not only to master the theory, but also to apply the knowledge gained in practice. A special place is occupied by the history of the development of the topic, which helps to understand how the ideas of trigonometric and orthogonal series have evolved and why they remain relevant in modern research. In general, this book is not just a collection of theoretical calculations, but a full-fledged scientific guide that stimulates further development and research. It will be useful to those who appreciate deep analysis, scientific novelty and practical significance. The author's style, characteristic of collective works, combines the rigor of scientific arguments with the clarity of presentation, which makes the book available both for specialists and for those who are just beginning to get acquainted with this area. Within the framework of the series "Modern Problems of Mathematics of Mechanics" it occupies a special place, combining the theoretical foundations with the current tasks of modern science. If you are looking for a book that will help you understand the complex mathematical structures associated with trigonometric and orthogonal series, and at the same time give you the opportunity to apply this knowledge in mechanics and physics, then “Modern Problems of Mathematics of Mechanics . T. 10. Mathematics. Issue. 1. For the 60th anniversary of the seminar" will become an indispensable assistant for you . This publication is a real treasure for those who seek to remain at the forefront of scientific research and expand the boundaries of their knowledge in the field of modern mathematics and mechanics.