Sequence Space Theory with Applications
Sequence Space Theory with Applications

Author: S. A. Mohiuddine

Publisher: CRC Press

Published: 2022-07-20

Total Pages: 307

ISBN-13: 1000610047

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The book features original chapters on sequence spaces involving the idea of ideal convergence, modulus function, multiplier sequences, Riesz mean, Fibonacci difference matrix etc., and illustrate their involvement in various applications. The preliminaries have been presented in the beginning of each chapter and then the advanced discussion takes place, so it is useful for both expert and nonexpert on aforesaid topics. The book consists of original thirteen research chapters contributed by the well-recognized researchers in the field of sequence spaces with associated applications. Features Discusses the Fibonacci and vector valued difference sequence spaces Presents the solution of Volterra integral equation in Banach algebra Discusses some sequence spaces involving invariant mean and related to the domain of Jordan totient matrix Presents the Tauberian theorems of double sequences Discusses the paranormed Riesz difference sequence space of fractional order Includes a technique for studying the existence of solutions of infinite system of functional integro-differential equations in Banach sequence spaces The subject of book is an active area of research of present time internationally and would serve as a good source for researcher and educators involved with the topic of sequence spaces.

Advances in Sequence Analysis: Theory, Method, Applications
Advances in Sequence Analysis: Theory, Method, Applications

Author: Philippe Blanchard

Publisher: Springer

Published: 2014-07-02

Total Pages: 308

ISBN-13: 3319049690

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This book gives a general view of sequence analysis, the statistical study of successions of states or events. It includes innovative contributions on life course studies, transitions into and out of employment, contemporaneous and historical careers, and political trajectories. The approach presented in this book is now central to the life-course perspective and the study of social processes more generally. This volume promotes the dialogue between approaches to sequence analysis that developed separately, within traditions contrasted in space and disciplines. It includes the latest developments in sequential concepts, coding, atypical datasets and time patterns, optimal matching and alternative algorithms, survey optimization, and visualization. Field studies include original sequential material related to parenting in 19th-century Belgium, higher education and work in Finland and Italy, family formation before and after German reunification, French Jews persecuted in occupied France, long-term trends in electoral participation, and regime democratization. Overall the book reassesses the classical uses of sequences and it promotes new ways of collecting, formatting, representing and processing them. The introduction provides basic sequential concepts and tools, as well as a history of the method. Chapters are presented in a way that is both accessible to the beginner and informative to the expert.

Ideal Sequence Design in Time-Frequency Space
Ideal Sequence Design in Time-Frequency Space

Author: Myoung An

Publisher: Springer Science & Business Media

Published: 2008-11-09

Total Pages: 237

ISBN-13: 0817647384

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This book develops theory and algorithms leading to systematic waveform design in time-frequency space. The key tool employed in the work is the Zak transform, which provides a two-dimensional image for sequences, the Fourier transform, convolution, and correlation, and allows for the design of sequences directly in Zak space. Application areas covered include pulse radars and sonars, multibeam radar and sonar imaging systems, remote dielectric material identification, and code division multiple-access communication systems. This is an excellent reference text for graduate students, researchers, and engineers in radar, sonar, and communication systems.

Approximation Theory, Sequence Spaces and Applications
Approximation Theory, Sequence Spaces and Applications

Author: S. A. Mohiuddine

Publisher: Springer Nature

Published: 2022-12-07

Total Pages: 277

ISBN-13: 9811961166

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This book publishes original research chapters on the theory of approximation by positive linear operators as well as theory of sequence spaces and illustrates their applications. Chapters are original and contributed by active researchers in the field of approximation theory and sequence spaces. Each chapter describes the problem of current importance and summarizes ways of their solution and possible applications which improve the current understanding pertaining to sequence spaces and approximation theory. The presentation of the articles is clear and self-contained throughout the book.

Sequence Spaces
Sequence Spaces

Author: Mohammad Mursaleen

Publisher: CRC Press

Published: 2020-03-10

Total Pages: 313

ISBN-13: 1000045153

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This book is aimed at both experts and non-experts with an interest in getting acquainted with sequence spaces, matrix transformations and their applications. It consists of several new results which are part of the recent research on these topics. It provides different points of view in one volume, e.g. their topological properties, geometry and summability, fuzzy valued study and more. This book presents the important role sequences and series play in everyday life, it covers geometry of Banach Sequence Spaces, it discusses the importance of generalized limit, it offers spectrum and fine spectrum of several linear operators and includes fuzzy valued sequences which exhibits the study of sequence spaces in fuzzy settings. This book is the main attraction for those who work in Sequence Spaces, Summability Theory and would also serve as a good source of reference for those involved with any topic of Real or Functional Analysis.

Topics in Banach Space Theory
Topics in Banach Space Theory

Author: Fernando Albiac

Publisher: Springer

Published: 2016-07-19

Total Pages: 512

ISBN-13: 3319315579

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This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Operators Between Sequence Spaces and Applications
Operators Between Sequence Spaces and Applications

Author: Bruno de Malafosse

Publisher: Springer Nature

Published: 2021-01-19

Total Pages: 379

ISBN-13: 9811597421

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This book presents modern methods in functional analysis and operator theory along with their applications in recent research. The book also deals with the solvability of infinite systems of linear equations in various sequence spaces. It uses the classical sequence spaces, generalized Cesaro and difference operators to obtain calculations and simplifications of complicated spaces involving these operators. In order to make it self-contained, comprehensive and of interest to a larger mathematical community, the authors have presented necessary concepts with results for advanced research topics. This book is intended for graduate and postgraduate students, teachers and researchers as a basis for further research, advanced lectures and seminars.

Summability Theory and Its Applications
Summability Theory and Its Applications

Author: Feyzi Başar

Publisher: CRC Press

Published: 2022-06-27

Total Pages: 521

ISBN-13: 1000599140

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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.

Sequences and Series in Banach Spaces
Sequences and Series in Banach Spaces

Author: J. Diestel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 273

ISBN-13: 1461252008

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This volume presents answers to some natural questions of a general analytic character that arise in the theory of Banach spaces. I believe that altogether too many of the results presented herein are unknown to the active abstract analysts, and this is not as it should be. Banach space theory has much to offer the prac titioners of analysis; unfortunately, some of the general principles that motivate the theory and make accessible many of its stunning achievements are couched in the technical jargon of the area, thereby making it unapproachable to one unwilling to spend considerable time and effort in deciphering the jargon. With this in mind, I have concentrated on presenting what I believe are basic phenomena in Banach spaces that any analyst can appreciate, enjoy, and perhaps even use. The topics covered have at least one serious omission: the beautiful and powerful theory of type and cotype. To be quite frank, I could not say what I wanted to say about this subject without increasing the length of the text by at least 75 percent. Even then, the words would not have done as much good as the advice to seek out the rich Seminaire Maurey-Schwartz lecture notes, wherein the theory's development can be traced from its conception. Again, the treasured volumes of Lindenstrauss and Tzafriri also present much of the theory of type and cotype and are must reading for those really interested in Banach space theory.

Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations
Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations

Author: Józef Banaś

Publisher: Springer

Published: 2014-07-18

Total Pages: 323

ISBN-13: 8132218868

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This book deals with the study of sequence spaces, matrix transformations, measures of noncompactness and their various applications. The notion of measure of noncompactness is one of the most useful ones available and has many applications. The book discusses some of the existence results for various types of differential and integral equations with the help of measures of noncompactness; in particular, the Hausdorff measure of noncompactness has been applied to obtain necessary and sufficient conditions for matrix operators between BK spaces to be compact operators. The book consists of eight self-contained chapters. Chapter 1 discusses the theory of FK spaces and Chapter 2 various duals of sequence spaces, which are used to characterize the matrix classes between these sequence spaces (FK and BK spaces) in Chapters 3 and 4. Chapter 5 studies the notion of a measure of noncompactness and its properties. The techniques associated with measures of noncompactness are applied to characterize the compact matrix operators in Chapters 6. In Chapters 7 and 8, some of the existence results are discussed for various types of differential and integral equations, which are obtained with the help of argumentations based on compactness conditions.