This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Upper-level undergraduates or beginning graduate students in mathematics; engineering or physics graduate students.
Maße
Höhe: 235 mm
Breite: 157 mm
Dicke: 15 mm
Gewicht
ISBN-13
978-981-4273-34-3 (9789814273343)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
New Mexico State Univ, Usa
Normed Linear and Banach Spaces; Linear Operators; Quotient Spaces; Finite Dimensional Normed Spaces; Inner Product and Hilbert Spaces; The Hahn-Banach Theorem; Applications of the Hahn-Banach Theorem to Normed Spaces; The Uniform Boundedness Principle; Weak Convergence; The Open Mapping and Closed Graph Theorems; Projections; Schauder Basis; Transpose and Adjoints of Continuous Linear Operators; Compact Operators; The Fredholm Alternative; The Spectrum of an Operator; Subdivisions of the Spectrum; The Spectrum of a Compact Operator; Symmetric Linear Operators; The Spectral Theorem for Compact Symmetric Operators; Symmetric Operators with Compact Inverse; Bounded Self Adjoint Operators; Orthogonal Projections; Sesquilinear Functionals; The Spectral Theorem for Bounded Self Adjoint Operators; An Operational Calculus.
