Download An Introductory Course in Summability Theory by Ants Aasma,Hemen Dutta,P. N. Natarajan PDF

By Ants Aasma,Hemen Dutta,P. N. Natarajan

An introductory direction in summability conception for college students, researchers, physicists, and engineers

In developing this e-book, the authors’ cause used to be to supply graduate scholars, researchers, physicists, and engineers with a cheap creation to summability concept. Over the process 9 chapters, the authors conceal the entire primary ideas and equations informing summability conception and its functions, in addition to a few of its lesser identified features. Following a quick advent to the historical past of summability idea, common matrix equipment are brought, and the Silverman-Toeplitz theorem on commonplace matrices is mentioned. various particular summability tools, together with the Nörlund procedure, the Weighted suggest procedure, the Abel technique, and the (C, 1) - technique are subsequent tested. a complete bankruptcy is dedicated to a dialogue of a few simple Tauberian theorems related to sure summability equipment. Following this are chapters dedicated to matrix transforms of summability and absolute summability domain names of reversible and common equipment; the concept of an ideal matrix process; matrix transforms of summability and absolute summability domain names of the Cesàro and Riesz equipment; convergence and the boundedness of sequences with pace; and convergence, boundedness, and summability with speed.

• Discusses effects on matrix transforms of a number of matrix methods

• the single English-language textbook describing the notions of convergence, boundedness, and summability with velocity, in addition to their purposes in approximation theory

• Compares the approximation orders of Fourier expansions in Banach areas via various matrix methods

• Matrix transforms of summability domain names of standard excellent matrix equipment are examined

• each one bankruptcy comprises numerous solved examples and end-of-chapter workouts, together with tricks for solutions

An Introductory direction in Summability concept is the suitable first textual content in summability concept for graduate scholars, specifically these having an exceptional take hold of of actual and intricate research. it's also a useful reference for arithmetic researchers and for physicists and engineers who paintings with Fourier sequence, Fourier transforms, or analytic continuation.

ANTS AASMA, PhD, is affiliate Professor of Mathematical Economics within the division of Economics and Finance at Tallinn collage of expertise, Estonia.

HEMEN DUTTA, PhD, is Senior Assistant Professor of arithmetic at Gauhati collage, India.

P.N. NATARAJAN, PhD, is previously Professor and Head of the dept of arithmetic, Ramakrishna challenge Vivekananda collage, Chennai, Tamilnadu, India.

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