Bøger i Frontiers in Mathematics serien

This book offers a systematic treatment of a classic topic in Analysis. Written in an accessible style and with proofs given as clearly as possible, it is a valuable resource for graduate students in Mathematical Analysis and researchers dealing with Hoelder-continuous functions and their applications.

The purpose of this book is to develop the foundations of the theory of holomorphicity on the ring of bicomplex numbers. Accordingly, the main focus is on expressing the similarities with, and differences from, the classical theory of one complex variable. The result is an elementary yet comprehensive introduction to the algebra, geometry and analysis of bicomplex numbers.Around the middle of the nineteenth century, several mathematicians (the best known being Sir William Hamilton and Arthur Cayley) became interested in studying number systems that extended the field of complex numbers. Hamilton famously introduced the quaternions, a skew field in real-dimension four, while almost simultaneously James Cockle introduced a commutative four-dimensional real algebra, which was rediscovered in 1892 by Corrado Segre, who referred to his elements as bicomplex numbers. The advantages of commutativity were accompanied by the introduction of zero divisors, something thatfor a while dampened interest in this subject. In recent years, due largely to the work of G.B. Price, there has been a resurgence of interest in the study of these numbers and, more importantly, in the study of functions defined on the ring of bicomplex numbers, which mimic the behavior of holomorphic functions of a complex variable.While the algebra of bicomplex numbers is a four-dimensional real algebra, it is useful to think of it as a ¿complexification¿ of the field of complex numbers; from this perspective, the bicomplex algebra possesses the properties of a one-dimensional theory inside four real dimensions. Its rich analysis and innovative geometry provide new ideas and potential applications in relativity and quantum mechanics alike. The book will appeal to researchers in the fields of complex, hypercomplex and functional analysis, as well as undergraduate and graduate students with an interest in one-or multidimensional complex analysis.

The focus of the book is on direct sums of CS-modules and classes of modules related to CS-modules, such as relative (injective) ejective modules, (quasi) continuous modules, and lifting modules.

This book gives an introduction to the field of Incidence Geometry by discussing the basic families of point-line geometries and introducing some of the mathematical techniques that are essential for their study.

Accessible to anyone with a basic knowledge of ring and module theoryA short introduction to torsion-free Abelian groups is included

This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given.

This book gives a unified representation of generalizations of the Schwarz Lemma. It examines key coefficient theorems of the last century and explains the connection between coefficient estimates and characteristics of the hyperbolic geometry in a domain.

This book documents the rich structure of the holomorphic Q function spaces which are geometric because they transform naturally under conformal mappings, emphasizing recent development based on interaction between geometric function and measure theory, and other branches of mathematical analysis.

Dedicated to the Russian mathematician Albert Shiryaev on his 70th birthday, this is a collection of papers written by his former students, co-authors and colleagues. The diversity of topics and comprehensive style of the papers make the book attractive for Ph.D.

This monograph provides a full discussion of flag-transitive Steiner designs, a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines.

This book offers a complete proof of the Fundamental Theorem of q-Clan Geometry, followed by a detailed study of the known examples. It completely works out the collineation groups of the associated generalized quadrangles and the stabilizers of their associated ovals.

The schemes are analyzed regarding their nonlinear stabilityRecently developed entropy schemes are presentedA formalism is introduced for source terms

Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory.

Regular rings were originally introduced by John von Neumann to clarify aspects of operator algebras ([33], [34], [9]). Goodearl ([14]) gives an extensive account of various types of regular rings and there exist several papers studying modules over regular rings ([27], [31], [15]).

This book highlights important developments on artinian modules over group rings of generalized nilpotent groups.

For instance, it seeks a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. The text probes similar questions for other elliptic operators, such as Schrodinger, and explores optimal composites and optimal insulation problems in terms of eigenvalues.

Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.

This book is concerned with the study of infinite matrices and their approximation by matrices of finite size. Concrete examples are used to illustrate the results throughout, including discrete Schroedinger operators and integral and boundary integral operators arising in mathematical physics and engineering.

This book presents research on the latest developments in differential geometry of lightlike (degenerate) subspaces. The main focus is on hypersurfaces and a variety of submanifolds of indefinite Kahlerian, Sasakian and quaternion Kahler manifolds.

The projectible symbol induces a (possibly non-linear and partially de ned) connection which lifts the observation process to the state space and gives a decomposition of the operator on the state space and of the noise.

This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation.

A functional identity can be informally described as an identical relation involving arbitrary elements in an associative ring together with arbitrary (unknown) functions. The book is accessible to a wide audience and touches on a variety of mathematical areas such as ring theory, algebra and operator theory.

Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules.

This book investigates the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges, considering this problem both for linear and quasi-linear equations.

This book offers basic theory on hypercomplex-analytic automorphic forms and functions for arithmetic subgroups of the Vahlen group in higher dimensional spaces. It establishes explicit relationships to generalized variants of the Riemann zeta function and Dirichlet L-series, and introduces hypercomplex multiplication of lattices.

A monograph that classifies finite generalized quadrangles by symmetry, generalizing the celebrated Lenz-Barlotti classification for projective planes. It introduces combinatorial, geometrical and group-theoretical concepts that arise in the classification and in the general theory of finite generalized quadrangles.

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. The book further contains many original PDE problems originating in biosciences.

This book covers invariant probabilities for a large class of discrete-time homogeneous Markov processes known as Feller processes. From the reviews:"A very useful reference for researchers wishing to enter the area of stationary Markov processes both from a probabilistic and a dynamical point of view."

If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C.