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Summability Theory and Its Applications
Summability Theory and Its Applications explains various aspects of summability and demonstrates its applications in a rigorous and coherent manner. The content can readily serve as a reference or as a useful series of lecture notes on the subject. This substantially revised new edition includes brand new material across several chapters as well as several corrections, including: the addition of the domain of Cesaro matrix C(m) of order m in the classical sequence spaces to Chapter 4; and introducing the domain of four-dimensional binomial matrix in the spaces of bounded, convergent in the Pringsheim's sense, both convergent in the Pringsheim's sense and bounded, and regularly convergent double sequences, in Chapter 7. Features Investigates different types of summable spaces and computes their dual Suitable for graduate students and researchers with a (special) interest in spaces of single and double sequences, matrix transformations and domains of triangle matrices Can serve as a reference or as supplementary reading in a computational physics course, or as a key text for special Analysis seminars.
Banach Limit and Applications
Banach Limit and Applications provides all the results in the area of Banach Limit, its extensions, generalizations, and applications to various fields in one go (as far as possible). All the results in this field, after Banach introduced this concept in 1932, were scattered till now. Sublinear functionals generating and dominating Banach Limit, unique Banach Limit (almost convergence), invariant means and invariant limits, absolute and strong almost convergence, applications to ergodicity, law of large numbers, Fourier series, uniform distribution of sequences, uniform density, core theorems, and functional Banach limits are discussed in this book. The discovery of functional analysis, such...
Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties
The aim of Summable Spaces and Their Duals, Matrix Transformations and Geometric Properties is to discuss primarily about different kinds of summable spaces, compute their duals and then characterize several matrix classes transforming one summable space into other. The book also discusses several geometric properties of summable spaces, as well as dealing with the construction of summable spaces using Orlicz functions, and explores several structural properties of such spaces. Each chapter contains a conclusion section highlighting the importance of results, and points the reader in the direction of possible new ideas for further study. Features Suitable for graduate schools, graduate students, researchers and faculty, and could be used as a key text for special Analysis seminars Investigates different types of summable spaces and computes their duals Characterizes several matrix classes transforming one summable space into other Discusses several geometric properties of summable spaces Examines several possible generalizations of Orlicz sequence spaces
Four Topics in Mathematics
This is a collection of four large papers in mathematics decoted to the memory of Professor Hisao Tominaga.
