Due 2020-01-30
1st ed. 2019, Approx. 140 p.
Printed book
Softcover
ISBN 978-3-030-32944-0
Includes a streamlined introduction to the duality theory of locally convex
spaces, culminating in the Mackey-Arens theorem
Treats various important topics concerning the weak topology of Banach spaces
Discusses examples of function spaces which occur in applications to
differential operators and measure theory
Provides as a highlight the treatment of weak compactness in L_1-spaces
This book provides an introduction to the theory of topological vector spaces, with a focus on
locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens
theorem, and also examines the properties of the weak topology on Banach spaces, for
instance Banachfs theorem on weak*-closed subspaces on the dual of a Banach space (alias
the Krein-Smulian theorem), the Eberlein-Smulian theorem, Kreinfs theorem on the closed
convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem
characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally
convex final topology, with the application to test functionsD() and the space of distributions,
and the Krein-Milman theorem. The book adopts an geconomich approach to interesting topics,
and avoids exploring all the arising side topics. Written in a concise mathematical style, it is
intended primarily for advanced graduate students with a background in elementary functional
analysis, but is also useful as a reference text for established mathematicians.
Due 2020-02-05
1st ed. 2019, Approx. 240 p.
Printed book
Hardcover
ISBN 978-981-15-1152-3
Collects research papers and survey articles on major topics in mathematical
analysis and its applications
Discusses recent advances in mathematical analysis, approximation theory,
fixed-point theory, and summability theory
Presents analytical techniques to solve problems and derive numerical solutions
This book collects original research papers and survey articles presented at the International
Conference on Recent Advances in Pure and Applied Mathematics (ICRAPAM), held at Delhi
Technological University, India, on 23?25 October 2018. Divided into two volumes, it discusses
major topics in mathematical analysis and its applications, and demonstrates the versatility and
inherent beauty of analysis. It also shows the use of analytical techniques to solve problems
and, wherever possible, derive their numerical solutions. This volume addresses major topics,
such as operator theory, approximation theory, fixed-point theory, holomorphic functions,
summability theory, and analytic functions. It is a valuable resource for students as well as
researchers in mathematical sciences.
Due 2020-02-19
1st ed. 2020, X, 170 p.
Printed book
Softcover
ISBN 978-3-030-32405-6
- Offers a comprehensive, structured treatment of the theory in both finitedimensional
and infinite-dimensional settings
- Includes numerous applications of multilinear operator integral techniques,
of interest to a broad audience
- This is the first book of its kind in terms of its subject, scope and style of exposition
This book provides a comprehensive treatment of multilinear operator integral techniques. The
exposition is structured to be suitable for a course on methods and applications of multilinear
operator integrals and also as a research aid. The ideas and contributions to the field are
surveyed and up-to-date results and methods are presented. Most practical constructions of
multiple operator integrals are included along with fundamental technical results and major
applications to smoothness properties of operator functions (Lipschitz and Holder continuity,
differentiability), approximation of operator functions, spectral shift functions, spectral flow in
the setting of noncommutative geometry, quantum differentiability, and differentiability of
noncommutative L^p-norms. Main ideas are demonstrated in simpler cases, while more
involved, technical proofs are outlined and supplemented with references. Selected open
problems in the field are also presented.
April 2020
Pages: 512
This book provides a research-expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert space valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramer and Karhunen classes as well as the stationary class. A new type of the Radon?Nikodym derivative of a Banach space valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.
Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong large numbers. Generalizations are made to consider Banach space valued stochastic processes to include processes of pth order for p ? 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.
This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Introduction and Preliminaries
Hilbert Modules and Covariance Kernels
Stochastic Measures and Operator Valued Bimeasures
Radon?Nikodym Derivatives and Schauder Basic Measures
Multidimensional Stochastic Processes
Special Topics
Applications
Generalizations
Graduate students in mathematics, probabilists, statisticians, functional analysts, communication engineers and physicists.