Series: Operator Theory: Advances and Applications, Vol. 261
1st ed. 2017, Approx. 500 p.
Printed book
Hardcover
ISBN 978-3-319-59077-6
* Provides surveys and original papers by internationally recognized authors
* Presents Victor Havin's mathematical heritage and describes life
during the former Soviet Union regime
* Includes a number of photographs never published before
This volume presents a collection of surveys and original papers in harmonic and complex
analysis, function spaces, and related topics, authored by internationally recognized
experts in the fields in honor of Victor Havin (1933-2015). It also features a scientific
biography of Havin, the leading analysis specialist of the middle of 20th century and
founder of the Saint Petersburg Analysis Seminar. A complete list of his publications,
as well as his public speech "Mathematics as a source of certainty and uncertainty",
presented at the Doctor Honoris Causa ceremony at Linkoping University, are also
included. A number of photographs illustrate Havin's biography.
396pp Apr 2017
ISBN: 978-1-78634-333-8 (hardcover)
ISBN: 978-1-78634-334-5 (softcover)
About This Book
This book constitutes a concise introductory course on Functional Analysis for students who have studied calculus and linear algebra. The topics covered are Banach spaces, continuous linear transformations, Frechet derivative, geometry of Hilbert spaces, compact operators, and distributions. In addition, the book includes selected applications of functional analysis to differential equations, optimization, physics (classical and quantum mechanics), and numerical analysis. The book contains 197 problems, meant to reinforce the fundamental concepts. The inclusion of detailed solutions to all the exercises makes the book ideal also for self-study.
A Friendly Approach to Functional Analysis is written specifically for undergraduate students of pure mathematics and engineering, and those studying joint programmes with mathematics.
Normed and Banach Spaces
Continuous and Linear Maps
Differentiation
Geometry of Inner Product Spaces
Compact Operators
A Glimpse of Distribution Theory
Graduate students in functional analysis, operator theory and mathematical physics.
230pp Feb 2018
ISBN: 978-981-3221-26-0 (hardcover)
This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.
Operator Functions of One and Two Operator Arguments
Spectrum Perturbations
Representations of Solutions to Operator Equations in Banach Spaces
Solution Estimates
Sylvester Equation
Diagonalizable Operators and Condition Numbers
Rotation of Eigenvectors
Triangular Representations of Operators
Undergraduate and graduate students, and researchers in matrix theory, functional analysis and their applications to differential and difference equations.
490pp May 2018
ISBN: 978-981-3220-78-2 (hardcover)
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.
This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
Analysis
Algebraic Topology, Specifically K-Theory and Cohomology
Equivariant Bordism
Existence of Metrics of Positive Scalar Curvature on Spin Manifolds
Auxiliary Material
Graduate students and researchers interested in global analysis, geometry, and topology.