Determining the invariant subspaces of any given transformation and writing the transformation as an integral in terms of invariant subspaces is a fundamental problem. This book presents the foundations of the theory of triangular and Jordan representation
Determining the invariant subspaces of any given transformation and writing the transformation as an integral in terms of invariant subspaces is a fun...
Intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area, this text differs from other problem books in the greater difficulty of the problems, some of which are well-known theorems in analysis. Nonetheless, no special preparation is required to solve the majority of the problems. Brief but detailed solutions to most of the problems are given in the second part of the book. The authors have aimed to systematize a range of problems that are found in sources that are almost inaccessible (especially to students) and in...
Intended for students wishing to deepen their knowledge of mathematical analysis and for those teaching courses in this area, this text differs from o...
Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This work starts with basic notions of homotopy theory and then introduces the axioms of generalized (co)homology
Aims to give an exposition of generalized (co)homology theories that can be read by mathematicians who are not experts in algebraic topology. This wor...
There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In...
There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to kn...
This is the first of three volumes on algebraic geometry. Most algebraic geometers are well-versed in the language of schemes, but many newcomers are still initially hesitant about them. Ueno's book provides an introduction to the theory, which should overcome any such impediment to learning this rich subject.
This is the first of three volumes on algebraic geometry. Most algebraic geometers are well-versed in the language of schemes, but many newcomers are ...
This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and...
This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, inva...
This volume presents the analysis of optimal control problems for systems described by partial differential equations. The book offers simple and clear exposition of main results in this area. The methods proposed by the author cover cases where the controlled system corresponds to well-posed or ill-posed boundary value problems, which can be linear or nonlinear. The uniqueness problem for the solution of nonlinear optimal control problems is analyzed in various settings. Solutions of several previously unsolved problems are given. In addition, general methods are applied to the study of two...
This volume presents the analysis of optimal control problems for systems described by partial differential equations. The book offers simple and clea...
The aim of this work is to develop the tool of logical deduction schemata and use it to establish upper and lower bounds on the complexity of proofs and their transformations in axiomatized theories. The main results are: establishment of upper bounds on the elongation of deductions in cut eliminations; a proof that the length of a direct deduction of an existence theorem in the predicate calculus cannot be bounded above by an elementary function of the length of an indirect deduction of the same theorem; a complexity version of the existence property of the constructive predicate calculus;...
The aim of this work is to develop the tool of logical deduction schemata and use it to establish upper and lower bounds on the complexity of proofs a...
Suitable for engineering and/or statistics students, communications engineers, and mathematicians, this book presents a firm theoretic basis of source coding (or data compression) in information theory. It describes universal coding methods - the methods t
Suitable for engineering and/or statistics students, communications engineers, and mathematicians, this book presents a firm theoretic basis of source...
The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, and the space of mappings.
The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field the...