Books in the North-Holland Mathematics Studies series

Presents a systematic and compact treatment of the qualitative theory of half-linear differential equations. This book covers such topics as oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations.

From a detailed analysis of hypercomplex numbers in up to four dimensions, Silviu Olariu presents hypercomplex number properties in five and six dimensions and on to an analysis of polar and planar hypercomplex numbers in n dimensions.

Studies automorphism groups of both graphs and maps. This book includes chapters on the subfields of enumerative topological graph theory and random topological graph theory, as well as on the composition of English church-bell music. It places emphasis on Cayley maps: imbeddings of Cayley graphs for finite groups.

Introduces a study of linear discrete parabolic problems through reducing the starting discrete problem to the Cauchy problem for an evolution equation in discrete time. This book contains a stability theory of discrete evolution equations in Banach space and gives applications of this theory to the analysis of modern discretization methods.

An introduction to the theory of bitopological spaces and its applications. It presents different families of subsets of bitopological spaces and various relations between two topologies are analyzed on one and the same set.

Devoted to various constructions of sets which are nonmeasurable with respect to invariant measures. This work begins by explaining the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense.

Attempts to develop a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. This work examines traditionally important problems, such as local and global existence of solutions and their properties.

There has been a common perception that computational complexity is a theory of 'bad news' because its typical results assert that various real-world and innocent-looking tasks are infeasible. This book takes a quantitative analysis of some of the major results in complexity that regard either classes of problems or individual concrete problems.

Aims to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y(t) = Ay(t) + u(t) that ends at the very frontier of research. This work includes applications to optimal diffusion processes; applications to optimal heat propagation processes; and more.

A monograph that provides a comprehensive treatment of expansion theorems for regular systems of first order differential equations and n-th order ordinary differential equations. It also provides a comprehensive treatment from abstract foundations to applications in physics and engineering. It focuses on non-self-adjoint problems.

The conference on Functional Analysis and Its Applications took place in Lviv, Ukraine and was dedicated to Polish mathematician Stefan Banach. This book contains scientific contributions of the conference participants, mostly in the areas of functional analysis, general topology, operator theory and related topics.

Contains 32 articles on various areas of functional analysis and its applications: Banach spaces and their geometry, operator ideals, Banach and operator algebras, operator and spectral theory, Frechet spaces and algebras, function and sequence spaces.

Shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. This work presents the theory of tensor norms as designed by Grothendieck in the Resume and deals with the relation between tensor norms and operator ideals.

Familiarizes both popular and fundamental notions and techniques from the theory of non-normed topological algebras with involution, demonstrating with examples and basic results the necessity of this perspective. This book focuses on the Hilbert-space (bounded) representation theory of topological algebras and their topological tensor products.

Presents the research developments in topological rings. This book includes exercises that illustrate results and theorems and also gives a comprehensive bibliography. It is aimed at those readers acquainted with some very basic point-set topology and algebra, in semester courses at the beginning graduate level or at advanced undergraduate level.

Contains a unitary and systematic presentation of parts of a fundamental branch of functional analysis: linear semigroup theory with main emphasis on examples and applications. This book includes several results referring to various classes of semigroups such as equicontinuous, compact, differentiable and analytic.

Covers the fundamental theorems in complex and functional analysis. This book includes generalized forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, and Lagrange Mean-Value Theorems.

The viability of a set K with respect to a given function (or multi-function) F, defined on it, describes the property that, for each initial data in K, the differential equation (or inclusion) driven by that function or multi-function) to have at least one solution. This book presents important concepts and results in viability and invariance.

Contains multiple proofs of several central results with a minor historical perspective. This book features: proof of Bieberbach conjecture (after DeBranges), material on asymptotic values, material on Natural Boundaries and a comprehensive introduction to entire and metomorphic functions.

Many problems for partial difference and integro-difference equations can be written as difference equations in a normed space. This book deals with the topic of linear and nonlinear difference equations in a normed space. It develops the freezing method and presents results on Volterra discrete equations.

Written with a view to provide basic tools for researchers working in Mathematical Analysis and Applications, concentrating on differential, integral and finite difference equations. This monograph is useful for those who are interested in learning or applying the inequalities with explicit estimates in their studies.

Provides developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. This book is application oriented and it contains the theory of Fractional Differential Equations. It provides problems and directions for further investigations.