Bøger i Grundlehren der mathematischen Wissenschaften serien

This book covers the fundamentals of convex analysis, a refinement of standard calculus with equalities and approximations replaced by inequalities. Reviews minimization algorithms, which provide immediate application to optimization and operations research.

A description of the global properties of simply-connected spaces that are non-positively curved in the sense of A. Part I provides an introduction to the geometry of geodesic spaces, while Part II develops the basic theory of spaces with upper curvature bounds.

This introduction to algebraic number theory discusses the classical concepts from the viewpoint of Arakelov theory. The treatment of class theory is particularly rich in illustrating complements, offering hints for further study, and providing concrete examples.

From its origins in the minimization of integral functionals, the notion of variations has evolved greatly in connection with applications in optimization, equilibrium, and control.

The German edition of this book appeared in 1932 under the title "Die gruppentheoretische Methode in der Quantenmechanik". This was possible because recent investigations in the theory of self-adjoint linear operators have made the mathematical foundation of Quantum Mechanics much clearer than it was in t 932.

With contributions by numerous experts

This book reviews higher dimensional Nevanlinna theory and its relationship with Diophantine approximation theory. Coverage builds up from the classical theory of meromorphic functions on the complex plane with full proofs, to the current state of research.

The field of optimal transport has made breathtaking forays into various other domains of mathematics. This book presents a broad overview of this area. PhD students or researchers can read the entire book without any prior knowledge of the field.

This book deals with condition as a main aspect in the understanding of the performance-regarding both stability and complexity-of numerical algorithms. It offers partial solutions for Smale's 17th problem.

The second volume of the Geometry of Algebraic Curves is devoted to the foundations of the theory of moduli of algebraic curves. Its authors are research mathematicians who have actively participated in the development of the Geometry of Algebraic Curves.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

The expanded second edition of this book reflects new developments including the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems and the Neistadt theory.