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Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators.

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.

This book provides an in depth discussion of Loewner's theorem on the characterization of matrix monotone functions.

In recent years there has been enormous activity in the theory of algebraic curves. Our goal is to give a comprehensive and self-contained account of the extrinsic geometry of algebraic curves, which in our opinion constitutes the main geometric core of the recent advances in curve theory.

The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

With contributions by numerous experts

It is a textbook for students, as well as a reference book for the working mathematician, on cohomological topics in number theory. New material is introduced here on duality theorems for unramified and tamely ramified extensions as well as a careful analysis of 2-extensions of real number fields.

This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems-such as those of geometric optics-of parts of the theory.

The representation theory of locally compact groups has been vig orously developed in the past twenty-five years or so; of the various branches of this theory, one of the most attractive (and formidable) is the representation theory of semi-simple Lie groups which, to a great extent, is the creation of a single man: Harish-Chandra.

Mehrere Grunde bewogen mich, den Plan zu einem Buch uber Quantenmechanik zu entwerfen, obwohl es in der Literatur schon manche Darstellung dieses Gebietes gibt. Einmal traf man bei den Lernenden immer wieder auf die Auf fassung, dass die Quantentheorie nur ein Provisorium der theoretischen Physik sei, aber zumindest noch einer genaueren Begrundung bedurfe, da sowohl der mathematische Formalismus nicht exakt fundiert sei als auch die physikalische Interpretion sehr nach Gefuhl in jedem Einzelfall durchgefuhrt wurde. Nachdem das Buch von J. v. NEu MANN, Mathematische Grundlagen der Quantenmechanik, vergriffen war, konnte man kaum ein entsprechendes Werk empfehlen, das im physikalischen Zusammenhang die mathematischen Grundlagen klar legt. In dem vorliegenden Buche ist die eigentiiche Quantenmechamk (also ohne Feldtheorie) in der Weise dargestellt, dass man sie als em mathematisch wohlbegrundetes und in sich genauso widerspruchs freies und abgeschlossenes System erkennt, wie die klassische Punkt mechanik. So wie die Krafte, d. h. so wie die HAMILTON-Funktwn, in der klassischen Mechanik gegeben sein mussen, so m der Quanten mechanik der HAMILTON-Uperator. Die Herleitung eines Ansatzes fur den HAMILTON-Operator eines Problems aus anderen Gebieten der Physik wird deshalb hier nicht naher begrundet. Neben dem Wunsch, die Quantenmechamk als ein in sich geschlos senes Gebiet darzustellen, bestand ein zweiter Grund fur die Abfassung des Buches in der inneren Harmonie zwischen mathematischer und physikalischer Struktur. Je grosser die abstrakte Schonheit einer Theo rie, desto grosser auch ihr Wahrheitsgehalt. Die innere Harmonie m der Struktur der Materie zu erkennen, d. h.

For a long time - at least from Fermat to Minkowski - the theory of quadratic forms was a part of number theory. On the basis of both - the number theory of quadratic forms and the ideas of modern algebra - Witt opened, in 1937, a new chapter in the theory of quadratic forms.

In Chapter 6, the results of Chapter'> 4 and 5 are applied to the study of optimal control problems for systems governed by evolution equations, when the control appears in the boundary conditions (so that non-homogeneous boundary value problems are the basic tool of this theory).

It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces.

This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author.

This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions.

g a largenumberof concrete ex amplesand factsnotavailablein other textbooks.

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory.

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.

From the reviews: "L.R. Shafarevich showed me the first edition [...] and said that this book will be from now on the book about class field theory. In fact it is by far the most complete treatment of the main theorems of algebraic number theory, including function fields over finite constant fields, that appeared in book form."

The usefulness of a joint consideration of classical theory of deterministic perturbations together with stochastic perturbations is illustrated in this section.