Dealing with the constructive Weierstrassian approach to the theory of function spaces and its various applications, this volume combines the advantages of atomic and wavelet representations to enhanced theories in spectral fractal elliptics and semi-linear equations.
Dealing with the constructive Weierstrassian approach to the theory of function spaces and its various applications, this volume combines the advantag...
Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development was and is the attempt at a theoretical synthesis of the entire body of physical knowledge. The main triumphs in physical science were, as a rule, associ ated with the various phases of this synthesis. The most radical expression of this tendency is the program of construction of a unified physical theory. After Maxwellian electrodynamics had unified the phenomena of electricity, magnetism, and optics in a single theoretical scheme on the basis...
Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development w...
Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such problems abound in applied mathematics, theoretical mechanics, and mathematical physics. This uncorrected soft cover reprint of the second edition places the emphasis on applications and presents a variety of techniques with extensive examples.Originally published in 1971, Linear Integral Equations is ideal as a text for a beginning graduate level course. Its treatment of boundary value problems also makes the book useful to researchers in...
Many physical problems that are usually solved by differential equation methods can be solved more effectively by integral equation methods. Such p...
Schrodinger Equations and Diffusion Theory addresses the question What is the Schrodinger equation? in terms of diffusion processes, and shows that the Schrodinger equation and diffusion equations in duality are equivalent. In turn, Schrodinger s conjecture of 1931 is solved. The theory of diffusion processes for the Schrodinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles.
The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion...
Schrodinger Equations and Diffusion Theory addresses the question What is the Schrodinger equation? in terms of diffusion processes, and sho...
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple definition a path on a lattice that does not visit the same site more than once it is difficult to analyze mathematically. TheSelf-Avoiding Walkprovides the firstunified account of the known rigorous results for the self-avoiding walk, with particular emphasis on its critical behavior. Its goals are to give an account of the current mathematical understanding of the model, to indicate some of the applications of the concept in physics...
The self-avoiding walk is a mathematical model that has important applications in statistical mechanics and polymer science. In spite of its simple...
These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are...
These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds ...
The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classification of Critical Points and originallypublishedas Volume82 in the Monographs in Mathematics series, contained the zoology of differentiable maps, that is, it was devoted to a description of what, where, and how singularities could be encountered, this second volume concentrates on elements of theanatomy and physiology of singularities of differentiable functions. The questions considered are about the structure of singularities and how...
The present volume is the second in a two-volume set entitled Singularities of Differentiable Maps. While the first volume, subtitled Classi...
This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature of the kernels involved is that they consist of unbounded linear operators. The aim is a coherentpresentation of the state of art of the theory including detailed proofs and its applications to problems from mathematical physics, such as viscoelasticity, heat conduction, and electrodynamics with memory. The importance of evolutionary integral equations which form a larger class than do evolution equations stems from such applications and...
This book deals with evolutionary systems whose equation of state can be formulated as a linear Volterra equation in a Banach space. The main feature ...
A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the most useful concepts for this purpose is that of the random walk which has applications in many areas, particularly in statistical physics and statistical chemistry.
Originally published in 1991, Intersections of Random Walks focuses on and explores a number of problems dealing primarily with the nonintersection of random walks and the self-avoiding walk. Many of these problems arise in studying statistical physics and other critical...
A central study in Probability Theory is the behavior of fluctuation phenomena of partial sums of different types of random variable. One of the mo...
The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis.
There are many different forms of the implicit function theorem, including (i) the classical formulation for Ck functions, (ii) formulations in other function spaces, (iii) formulations for non-smooth...
The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of re...
