Книга "Введение в теорию суммируемости" предназначена для студентов, исследователей, физиков и инженеров, желающих познакомиться с основными концепциями и уравнениями, связанными с теорией суммируемости. Авторы представляют девять глав, охватывающих все фундаментальные понятия и уравнения, определяющие теорию суммируемости и ее применения, а также некоторые менее известные аспекты. В книге рассматриваются методы суммируемости, включая метод Нерлунда, метод взвешенных средних, метод Абеля и метод (C, 1), а также элементарные теоремы Тобери, связанные с некоторыми методами суммируемости. Книга также описывает матричные преобразования суммируемости и абсолютной суммируемости, области суммируемости и абсолютной суммируемости нормальных методов, сходимость и ограниченность последовательностей со скоростью, а также сходимость, ограниченность и суммируемость со скоростью. Каждая глава содержит несколько примеров и упражнений с подсказками для решения. Книга является идеальным первым учебным пособием в теории суммируемости для аспирантов, особенно тех, кто хорошо владеет реальным и комплексным анализом. Книга также может быть полезна как справочник для математических исследователей, а также для физиков и инженеров, работающих с рядами Фурье, преобразованиями Фурье или аналитическим продолжением.
A preliminary memoranda for investigators in theoretical summation, by Hemen Datta. In constructing this compendium, the author's intent was clearly to provide undergraduate pupils, explorers, mathematicians, and informatics technicians with a sane introduction to theoretical summation. After the short introduction into the story of theoretical summation consolidated later the general matrix methodologies and the powerframework theorem upon conventional matricies are examine. As many particular summations utilising Veterans Bistro, the emphasised looks, the appended piece of information tackle, and the(C,1)-method are viewed. A sort of chapter is allocated to the discussion about some immediate Tauberi theorems that involve various sorts of obedience methods. Subsequent are sections emphasised to the changing of matricies of summality and separated bounds domains of invertible methods and normal conceivable methods; the occurrence of a precise matrix approach; matricies substitute whole objects and sparsity domains of bits Ceasar and Disposal methods; convert and the boundlessness of feelings with time; and change, arrowiness, and parallelism with answer.
Электронная Книга «An Introductory Course in Summability Theory» написана автором Hemen Dutta в году.
Минимальный возраст читателя: 0
Язык: Английский
ISBN: 9781119397731
Описание книги от Hemen Dutta
An introductory course in summability theory for students, researchers, physicists, and engineers In creating this book, the authors’ intent was to provide graduate students, researchers, physicists, and engineers with a reasonable introduction to summability theory. Over the course of nine chapters, the authors cover all of the fundamental concepts and equations informing summability theory and its applications, as well as some of its lesser known aspects. Following a brief introduction to the history of summability theory, general matrix methods are introduced, and the Silverman-Toeplitz theorem on regular matrices is discussed. A variety of special summability methods, including the Nörlund method, the Weighted Mean method, the Abel method, and the (C, 1) – method are next examined. An entire chapter is devoted to a discussion of some elementary Tauberian theorems involving certain summability methods. Following this are chapters devoted to matrix transforms of summability and absolute summability domains of reversible and normal methods; the notion of a perfect matrix method; matrix transforms of summability and absolute summability domains of the Cesàro and Riesz methods; convergence and the boundedness of sequences with speed; and convergence, boundedness, and summability with speed. • Discusses results on matrix transforms of several matrix methods • The only English-language textbook describing the notions of convergence, boundedness, and summability with speed, as well as their applications in approximation theory • Compares the approximation orders of Fourier expansions in Banach spaces by different matrix methods • Matrix transforms of summability domains of regular perfect matrix methods are examined • Each chapter contains several solved examples and end-of-chapter exercises, including hints for solutions An Introductory Course in Summability Theory is the ideal first text in summability theory for graduate students, especially those having a good grasp of real and complex analysis. It is also a valuable reference for mathematics researchers and for physicists and engineers who work with Fourier series, Fourier transforms, or analytic continuation. ANTS AASMA, PhD, is Associate Professor of Mathematical Economics in the Department of Economics and Finance at Tallinn University of Technology, Estonia. HEMEN DUTTA, PhD, is Senior Assistant Professor of Mathematics at Gauhati University, India. P.N. NATARAJAN, PhD, is Formerly Professor and Head of the Department of Mathematics, Ramakrishna Mission Vivekananda College, Chennai, Tamilnadu, India.
