This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.

Theories of Integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane (Series in Real Analysis)

Science & Math

Kurtz, Douglas S.

Swartz, Charles W.

Mathematics

World Scientific Publishing Company

If λ is a space of scalar-valued sequences, then a series ∑j xj in a topological vector space X is λ-multiplier convergent if the series ∑j=1∞ tjxj converges in X for every {tj} ελ. 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 ι1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.

MULTIPLIER CONVERGENT SERIES

The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock–Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.

THEORIES OF INTEGRATION: THE INTEGRALS OF RIEMANN, LEBESGUE, HENSTOCK-KURZWEIL, AND MCSHANE (SECOND EDITION) (Real Analysis)

A functional calculus is a construction which associates with an operator or a family of operators a homomorphism from a function space into a subspace of continuous linear operators, i.e. a method for defining "functions of an operator". Perhaps the most familiar example is based on the spectral theorem for bounded self-adjoint operators on a complex Hilbert space.This book contains an exposition of several such functional calculi. In particular, there is an exposition based on the spectral theorem for bounded, self-adjoint operators, an extension to the case of several commuting self-adjoint operators and an extension to normal operators. The Riesz operational calculus based on the Cauchy integral theorem from complex analysis is also described. Finally, an exposition of a functional calculus due to H. Weyl is given.

FUNCTIONAL CALCULI

BOSCH, CARLOS

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Books by Swartz, Charles W.

See the best price to sell, buy, or rent books by Swartz, Charles W.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Theories of Integration: The Integrals of Riemann, Lebesgue, Henstock-Kurzweil, and McShane (Series in Real Analysis)

MULTIPLIER CONVERGENT SERIES

THEORIES OF INTEGRATION: THE INTEGRALS OF RIEMANN, LEBESGUE, HENSTOCK-KURZWEIL, AND MCSHANE (SECOND EDITION) (Real Analysis)

FUNCTIONAL CALCULI