rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Concrete Functional Calculus
  name:
    name part: Dudley, R. M.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Norvaiša, R.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 671 p. online resource.
  abstract: Concrete Functional Calculus focuses primarily on differentiability of some nonlinear operators on functions or pairs of functions. This includes composition of two functions, and the product integral, taking a matrix- or operator-valued coefficient function into a solution of a system of linear differential equations with the given coefficients. For nonlinear integral equations with respect to possibly discontinuous functions having unbounded variation, existence and uniqueness of solutions are proved under suitable assumptions. Key features and topics: * Extensive usage of p-variation of functions * Applications to stochastic processes. This work will serve as a thorough reference on its main topics for researchers and graduate students with a background in real analysis and, for Chapter 12, in probability.
  table of contents: Preface -- 1 Introduction and Overview -- 2 Definitions and Basic Properties of Extended Riemann-Stieltjes Integrals -- 3 Phi-variation and p-variation; Inequalities for Integrals -- 4 Banach Algebras -- 5 Derivatives and Analyticity in Normed Spaces -- 6 Nemytskii Operators on Some Function Spaces -- 7 Nemytskii Oerators on Lp Spaces -- 8 Two-Function Composition -- 9 Product Integration -- 10 Nonlinear Differential and Integral Equations -- 11 Fourier Series -- 12 Stochastic Processes and Phi-Variation -- Appendix Nonatomic Measure Spaces -- References -- Subject Index -- Author Index -- Index of Notation.
  note: by R. M. Dudley, R. Norvaiša.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Integral equations
  subject:
    topic: Operator theory
  subject:
    topic: Functions of real variables
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Integral Equations
  subject:
    topic: Operator Theory
  subject:
    topic: Real Functions
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Springer Monographs in Mathematics
  identifier: 9781441969507
  identifier: http://dx.doi.org/10.1007/978-1-4419-6950-7
  record info:
    record creation date: 101109
    record change date: 20151116133428.0
    record identifier: 978-1-4419-6950-7