This work includes introductory materials on complex analysis of several variables and material on analytic theory of partial differential equations, as well as on nonanalytic boundary value problems for systems of partial differential equations of…
Presenting new results along with research spanning five decades, Fractional Cauchy Transforms provides a full treatment of the topic, from its roots in classical complex analysis to its current state. Self-contained, it includes introductory materi…
Presents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. Smooth Homogeneous Structures in Operator Theory builds the background needed to understand this circle of ideas and reports on recent deve…
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
The method of compensated compactness as a technique for studying hyperbolic conservation laws is of fundamental importance in many branches of applied mathematics. Until now, however, most accounts of this method have been confined to research pape…
Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that, in some cases, they may violate the laws of thermodynamics. In The Thermophysics of Porous Media, the…
This book provides a systematic exposition of the results related to periodic solutions of impulsive differential equations and illustrates the potential for their application by a large number of concrete mathematical models.
Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods…
This book studies the foundations of the general theory of generalized analytic functions in fractional spaces. The employment of fractional spaces and embedding theorems support applications of the theory of generalized analytic functions. The resu…
Nonlinearity plays a major role in the understanding of most physical, chemical, biological, and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often elude exact treatment. However elusive they may be, the solutions…
Although the study of classical thermoelasticity has provided information on linear systems, only recently have results on the asymptotic behavior completed our basic understanding of the generic behavior of solutions. Through systematic work that b…
This text provides a comprehensive treatment of representations on indefinite metric spaces, and their applications to the theory of *-derivations of C*-algebras. The book consists of two parts. The first studies the geometry of indefinite metric sp…
This volume provides an introduction to modern concepts of linear and nonlinear functional analysis. Its purpose is also to provide an insight into the variety of deeply interlaced mathematical tools applied in the study of nonlinear problems.
An American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computation…
Together with the authors' Volume I. C*-Theory, the two parts comprising Functional Differential Equations: II. C*-Applications form a masterful work-the first thorough, up-to-date exposition of this field of modern analysis lying between differenti…
Useful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various…
A theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book…
This Monograph contains a collection of problems arising in partial differential equations investigated by means of complex analysis approached in elementary ways.
The precise mathematical investigation of various natural phenomena is an old and difficult problem. This book is the first to deal systematically with the general non-selfadjoint problems in mechanics and physics. It deals mainly with bounded domai…
This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a s…
A continuation of the authors' previous book, Isometries on Banach Spaces: Vector-valued Function Spaces and Operator Spaces, Volume Two covers much of the work that has been done on characterizing isometries on various Banach spaces. Picking up whe…
In the view of many probabilists, author Anatolii Puhalskii's research results stand among the most significant achievements in the modern theory of large deviations. In fact, his work marked a turning point in the depth of our understanding of the…
Following Witten's remarkable discovery of the quantum mechanical scheme in which all the salient features of supersymmetry are embedded, SCQM (supersymmetric classical and quantum mechanics) has become a separate area of research . In recent years,…
Understanding the causes and effects of explosions is important to experts in a broad range of disciplines, including the military, industrial and environmental research, aeronautic engineering, and applied mathematics. Offering an introductory revi…
Module theory over commutative asociative rings is usually extended to noncommutative associative rings by introducing the category of left (or right) modules. An alternative to this procedure is suggested by considering bimodules. A refined module…
The International Society for the Interaction of Mechanics and Mathematics has a long-standing and respected tradition of hosting symposia that provide a forum for disseminating new developments and methods. Trends in Applications of Mathematics to…
Inverse boundary problems are a rapidly developing area of applied mathematics with applications throughout physics and the engineering sciences. However, the mathematical theory of inverse problems remains incomplete and needs further development t…
Although the analysis of scattering for closed bodies of simple geometric shape is well developed, structures with edges, cavities, or inclusions have seemed, until now, intractable to analytical methods. This two-volume set describes a breakthrough…
Interfacial phenomena driven by heat or mass transfer are widespread in science and various branches of engineering. Research in this area has become quite active in recent years, attributable in part, at least, to the entry of physicists and their…
This text uses complex and functional analytic methods to treat boundary value problems for non-linear equations and systems of first and higher order in multiply-connected plane domains. Also presented are applications in continuum mechanics.
This monograph investigates a wide range of problems where nonlinear wave phenomena play a crucial role, for instance in nonlinear acoustics, fluid dynamics, plasma physics and magnetohydrodynamics. The aim of the book is to deliver a general approa…
Systems of partial differential equations reflecting conservation laws hold significant relevance to a variety of theoretical and practical applications, including compressible fluid flow, electromagnetism, elasticity theory, and other areas of cont…
Although the theory behind solitary waves of strain shows that they hold significant promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable elastic solitary waves in practice. In…
This book introduces the class of dynamical systems called semiflows, which includes systems defined or modeled by certain types of differential evolution equations (DEEs). It focuses on the basic results of the theory of dynamical systems that can…
The Riemann problem is the most fundamental problem in the entire field of non-linear hyperbolic conservation laws. Since first posed and solved in 1860, great progress has been achieved in the one-dimensional case. However, the two-dimensional case…
A survey of some problems of current interest in the realm of classical nonlinear electromagnetic theory.
Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the -uniform convergence of these schemes and surveys the latest approaches impor…
Singular Partial Differential Equations provides an analytical, constructive, and elementary approach to non-elementary problems. In the first monograph to consider such equations, the author investigates the solvability of partial differential equa…
Extremality results proved in this Monograph for an abstract operator equation provide the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary…
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of s…
Elastic plates form a class of very important mechanical structures that appear in a wide range of practical applications, from building bodies to microchip production. As the sophistication of industrial designs has increased, so has the demand for…
A topic of major importance to engineers and physicists, the theory of distributions remains a difficult subject for the non-mathematician. This version of the theory presents a more natural approach.
The computational power currently available means that practitioners can find extremely accurate approximations to the solutions of more and more sophisticated mathematical models-providing they know the right analytical techniques. In relatively si…
Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation…
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been thr…