Functional analysis and transforms

This graduate textbook offers an introduction to the spectral theory of ordinary differential equations, focusing on Sturm-Liouville equations.

This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory.

A short introduction perfect for any 16- to 18-year-old, about to begin studies in mathematics.

The subject of this book is probabilistic number theory.

This book presents a method for evaluating Selberg zeta functions via transfer operators for the full modular group and its congruence subgroups with characters.

The present monograph is devoted to the construction and investigation of the new high order of accuracy difference schemes of approximating the solutions of regular and singular perturbation boundary value problems for partial differential equations.

The goal of this monograph is to prove that any solution of the Cauchy problem for the capillary-gravity water waves equations, in one space dimension, with periodic, even in space, small and smooth enough initial data, is almost globally defined in time on Sobolev spaces, provided the gravity-capillarity parameters are taken outside an exceptional subset of zero measure.

This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces.

This book offers a review of the theory of locally convex quasi *-algebras, authored by two of its contributors over the last 25 years.

The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography.

The focus of this monograph is the study of rings and modules which have a rich supply of direct summands with respect to various extensions.

This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1).

The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc.

Integrated operation of hydropower stations and reservoirs has become a trend of hydropower exploitation, as an effective technical measure, integrated operation can improve the utilization efficiency of water resources, reduce the risks of flood and drought disaster, increase the safety and stability power grid and make sure that hydropower stations and reservoirs operate in an appropriate and economical way.

- Follows a standard course curriculum.

The work consists of two introductory courses, developing different points of view on the study of the asymptotic behaviour of the geodesic flow, namely: the probabilistic approach via martingales and mixing (by Stephane Le Borgne); the semi-classical approach, by operator theory and resonances (by Frederic Faure and Masato Tsujii).

One of the fundamental questions of Banach space theory is whether every Banach space has a basis.

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields.

Fractional Integral Transforms: Theory and Applications presents over twenty-five integral transforms, many of which have never before been collected in one single volume.

Dynamical Systems Method for Solving Nonlinear Operator Equations is of interest to graduate students in functional analysis, numerical analysis, and ill-posed and inverse problems especially.

Thisvolumecontainsaselectionofpapersinmodernoperatortheoryanditsapp- cations.

Mathematical modeling plays an essential role in science and engineering.

This book is intended for university seniors and graduate students majoring in probability theory or mathematical finance.

This book provides comprehensive, graduate-level treatment of analog and digital signal analysis suitable for course use and self-guided learning.

This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions.

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century.

Although the monograph Progress in Optimization I: Contributions from Aus- tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza- tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization.

This book employs a computable general equilibrium (CGE) model - a widely used economic model which uses actual data to provide economic analysis and policy assessment - and applies it to economic data on Singapore's tourism industry.

In this volume we study the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis.

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces.

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces.

New edition of an introduction to Fourier transforms, invaluable to students in physics, electrical and electronic engineering, and computer science.

This book is an extensive introductory text to mathematical analysis for graduate students and advanced undergraduates, complete with 500 exercises and numerous examples.

This book was written expressly to serve as a textbook for a one- or two-semester introductory graduate course in functional analysis.

Partial Differential Equations: Topics in Fourier Analysis explains how to use the Fourier transform and heuristic methods to obtain significant insight into the solutions of standard PDE models.

This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting.

This monograph introduces a novel and effective approach to counting lattice paths by using the discrete Fourier transform (DFT) as a type of periodic generating function.

Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups.

This book represents the first synthesis of the considerable body of new research into positive definite matrices.

The equations of mathematical physics are the mathematical models of the large class of phenomenon of physics, chemistry, biology, economics, etc.

A thorough graduate-level introduction to the variational analysis of nonlinear problems described by nonlocal operators.

Advances in Discrete Tomography and Its Applications is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image reconstruction by discrete tomographic methods.