Infinite Matrices And The Gliding Hump

Author : Charles Swartz
Publisher : World Scientific
ISBN 13 : 9810227361
Total Pages : 222 pages
Book Rating : 4.64/5 ( download)

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Download or read book Infinite Matrices and the Gliding Hump written by Charles Swartz and published by World Scientific. This book was released on 1996 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

Author : Charles W Swartz
Publisher : World Scientific
ISBN 13 : 9814498718
Total Pages : 222 pages
Book Rating : 4.15/5 ( download)

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Download or read book Infinite Matrices And The Gliding Hump, Matrix Methods In Analysis written by Charles W Swartz and published by World Scientific. This book was released on 1996-08-22 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

Author : Richard G. Cooke
Publisher : Courier Corporation
ISBN 13 : 048678083X
Total Pages : 370 pages
Book Rating : 4.32/5 ( download)

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Download or read book Infinite Matrices and Sequence Spaces written by Richard G. Cooke and published by Courier Corporation. This book was released on 2014-07-16 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, correct summation of basic results on general behavior of infinite matrices features three introductory chapters leading to applications related to summability of divergent sequences and series. Nearly 200 examples. 1950 edition.

Author : Karl Sabbagh
Publisher : Macmillan
ISBN 13 : 9780374250072
Total Pages : 364 pages
Book Rating : 4.73/5 ( download)

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Download or read book The Riemann Hypothesis written by Karl Sabbagh and published by Macmillan. This book was released on 2003 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: An engaging, informative, and wryly humorous exploration of one of the great conundrums of all time In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article giving an answer to a problem that had long puzzled mathematicians. But he didn’t provide a proof. In fact, he said he couldn’t prove it but he thought that his answer was “very probably” true. From the publication of that paper to the present day, the world’s mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann Hypothesis, and so great is the interest in its solution that in 2001 an American foundation put up prize money of $1 million for the first person to demonstrate that the hypothesis is correct. The hypothesis refers to prime numbers, which are in some sense the atoms from which all other numbers are constructed, and seeks to explain where every single prime to infinity will occur. Riemann’s idea—if true—would illuminate how these numbers are distributed, and if false will throw pure mathematics into confusion. Karl Sabbagh meets some of the world’s mathematicians who spend their lives thinking about the Riemann Hypothesis, focusing attention in particular on “Riemann’s zeros,” a series of points that are believed to lie in a straight line, though no one can prove it. Accessible and vivid, The Riemann Hypothesis is a brilliant explanation of numbers and a profound meditation on the ultimate meaning of mathematics.

Author : Johann Boos
Publisher : Clarendon Press
ISBN 13 : 9780198501657
Total Pages : 616 pages
Book Rating : 4.5X/5 ( download)

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Download or read book Classical and Modern Methods in Summability written by Johann Boos and published by Clarendon Press. This book was released on 2000 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Summability is a mathematical topic with a long tradition and many applications in, for example, function theory, number theory, and stochastics. It was originally based on classical analytical methods, but was strongly influenced by modern functional analytical methods during the last seven decades. The present book aims to introduce the reader to the wide field of summability and its applications, and provides an overview of the most important classical and modern methods used. Part I contains a short general introduction to summability, the basic classical theory concerning mainly inclusion theorems and theorems of the Silverman-Toeplitz type, a presentation of the most important classes of summability methods, Tauberian theorems, and applications of matrix methods. The proofs in Part I are exclusively done by applying classical analytical methods. Part II is concerned with modern functional analytical methods in summability, and contains the essential functional analytical basis required in later parts of the book, topologization of sequence spaces as K- and KF-spaces, domains of matrix methods as FK-spaces and their topological structure. In this part the proofs are of functional analytical nature only. Part III of the present book deals with topics in summability and topological sequence spaces which require the combination of classical and modern methods. It covers investigations of the constistency of matrix methods and of the bounded domain of matrix methods via Saks space theory, and the presentation of some aspects in topological sequence spaces. Lecturers, graduate students, and researchers working in summability and related topics will find this book a useful introduction and reference work.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9401512795
Total Pages : 639 pages
Book Rating : 4.94/5 ( download)

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Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Author : Bernard Russo
Publisher : American Mathematical Soc.
ISBN 13 : 1470419289
Total Pages : 272 pages
Book Rating : 4.88/5 ( download)

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Download or read book Topics in Functional Analysis and Algebra written by Bernard Russo and published by American Mathematical Soc.. This book was released on 2016-08-25 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20–23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan. This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrödinger operators, convexity and dynamical systems.

Author : Charles Swartz
Publisher : World Scientific
ISBN 13 : 9812833870
Total Pages : 264 pages
Book Rating : 4.77/5 ( download)

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Download or read book Multiplier Convergent Series written by Charles Swartz and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: If ? is a space of scalar-valued sequences, then a series ?j xj in a topological vector space X is ?-multiplier convergent if the series ?j=1ì tjxj converges in X for every {tj} î?. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the Orlicz-Pettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical Hahn-Schur theorem on the equivalence of weak and norm convergent series in ?1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.

Author : Jacob Korevaar
Publisher : Springer Science & Business Media
ISBN 13 : 3662102250
Total Pages : 497 pages
Book Rating : 4.51/5 ( download)

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Download or read book Tauberian Theory written by Jacob Korevaar and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.

Author : Swartz Charles W
Publisher : World Scientific
ISBN 13 : 9813232781
Total Pages : 304 pages
Book Rating : 4.85/5 ( download)

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Download or read book Abstract Duality Pairs In Analysis written by Swartz Charles W and published by World Scientific. This book was released on 2017-12-20 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz–Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach–Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali–Hahn–Saks Theorem from measure theory and the Hahn–Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis. Contents: PrefaceAbstract Duality Pairs or Abstract TriplesSubseries ConvergenceBounded Multiplier Convergent SeriesMultiplier Convergent SeriesThe Uniform Boundedness PrincipleBanach–SteinhausBiadditive and Bilinear OperatorsTriples with ProjectionsWeak Compactness in TriplesAppendices: TopologySequence SpacesBoundedness CriterionDrewnowskiAntosik–Mikusinski Matrix TheoremsReferencesIndex Readership: Graduate Students and researchers in functional analysis. Keywords: Duality;Convergent Series;Orlicz-Pettis;Integrals;Measures;Sequence Spaces;Uniform BoundednessReview: Key Features: The book should be of interest to people with interests in functional analysisReaders should find interesting the many applications to various topics in real analysisThere are no books on the current market which cover the material in the book