Many problems in operator theory lead to the consideration ofoperator equa- tions, either directly or via some reformulation. More often than not, how- ever, the underlying space is too 'small' to contain solutions of these equa- tions and thus it has to be 'enlarged' in some way. The Berberian-Quigley enlargement of a Banach space, which allows one to convert approximate into genuine eigenvectors, serves as a classical example. In the theory of operator algebras, a C*-algebra A that turns out to be small in this sense tradition- ally is enlarged to its (universal) enveloping von Neumann...
Many problems in operator theory lead to the consideration ofoperator equa- tions, either directly or via some reformulation. More often than not, how...
Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques. The first part of the book, which should be regarded as an extended reference section, presents a survey of the results from functional analysis, the theory of positive operators and the theory of semigroups that are needed for the second, applied part of the book; worked examples are provided to help absorb the theoretical material. The second part then deals with the application of the developed...
Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on...
The aim of this book is to present an exposition of the theory of alge- braic numbers, excluding class-field theory and its consequences. There are many ways to develop this subject; the latest trend is to neglect the classical Dedekind theory of ideals in favour of local methods. However, for numeri- cal computations, necessary for applications of algebraic numbers to other areas of number theory, the old approach seems more suitable, although its exposition is obviously longer. On the other hand the local approach is more powerful for analytical purposes, as demonstrated in Tate's thesis....
The aim of this book is to present an exposition of the theory of alge- braic numbers, excluding class-field theory and its consequences. There are ma...
"Serre's Conjecture," for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the effect that one did not know if ?nitely generated projective modules were free over a polynomial ring k x, . . ., x], where k is a ?eld. This statement was motivated by the fact that 1 n the af?ne scheme de?ned by k x, . . ., x] is the algebro-geometric analogue of 1 n the af?ne n-space over k. In topology, the n-space is contractible, so there are only trivial bundles over it. Would the analogue of the latter also hold for the n-space in...
"Serre's Conjecture," for the most part of the second half of the 20th century, - ferred to the famous statement made by J. -P. Serre in 1955, to the ...
This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesting problems in partial and ordinary differential equations, differential geometry and mathematical physics as applications, and provides the necessary preparation for almost all important aspects in contemporary studies. All methods are illustrated by carefully chosen examples from mechanics, physics, engineering and geometry.
This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It review...
The theory of groups and Lie algebras is interesting for many reasons. In the mathematical viewpoint, it employs at the same time algebra, analysis and geometry. On the other hand, it intervenes in other areas of science, in particularindi?erentbranchesofphysicsandchemistry.Itisanactivedomain of current research. Oneofthedi?cultiesthatgraduatestudentsormathematiciansinterested in the theory come across, is the fact that the theory has very much advanced, andconsequently, theyneedtoreadavastamountofbooksandarticlesbefore they could tackle interesting problems. One of the goals we wish to...
The theory of groups and Lie algebras is interesting for many reasons. In the mathematical viewpoint, it employs at the same time algebra, analysis an...
The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or a scheme as we shall say brie?y), and in order to do so we ?x a set and call it X. We write 1 to denote the set of all pairs (x, x) with x? X. For each subset X ? r of the cartesian product XX, we de?ne r to be the set of all pairs (y, z) with (z, y)? r.For x an element of X and r a subset of X X, we shall denote by xr the set of all elements y in X with (x, y)? r. Let us ?x a partition S of XX with / S and 1 ? S, and let us assume X ? that s ? S for each element...
The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or a scheme as we shal...
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.
Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations...
Finite model theory, the model theory of finite structures, has roots in clas- sical model theory; however, its systematic development was strongly influ- enced by research and questions of complexity theory and of database theory. Model theory or the theory of models, as it was first named by Tarski in 1954, may be considered as the part of the semantics of formalized languages that is concerned with the interplay between the syntactic structure of an axiom system on the one hand and (algebraic, settheoretic, . . . ) properties of its models on the other hand. As it turned out, first-order...
Finite model theory, the model theory of finite structures, has roots in clas- sical model theory; however, its systematic development was strongly in...
In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems," it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact...
In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Ano...
