(Hardback)

Intended for students with a beginning knowledge of mathematical analysis, this first volume, in a three-part introduction to Fourier analysis, introduces the core areas of mathematical analysis while also illustrating the organic unity between them. It includes numerous examples and applications.

(Hardback)

Reciprocity laws of various kinds play a central role in number theory. This book states several reciprocity laws in terms of abelian varieties, theta functions, and modular functions of several variables, including Siegel modular functions. It also covers the zeta function of an abelian variety as a main theme.

(Paperback)

The purpose of this book is to describe a certain number of results involving the study of non-linear analytic dependence of some functionals arising naturally in P.D.E. or operator theory.

(Paperback)

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. This book realizes this by creating a logarithmic Hodge theory. It uses the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure.

(Paperback)

Presents readers with a coherent branch of nonlinear mathematical analysis that is suited to the study of optimization problems. This volume treats the topics such as: systems of inequalities, the minimum or maximum of a convex function over a convex set, Lagrange multipliers, minimax theorems and duality, and more.

(Paperback)

Focuses on the difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. This book provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions.

(Paperback)

Geometry of orthogonal spaces.

(Hardback)

(Paperback)

An investigation of finite Riemann surfaces from the point of view of functional analysis, that is, the study of the various Abelian differentials of the surface in their dependence on the surface itself. Many new results are presented. Originally published in 1954. The Princeton Legacy Library uses the latest print-on-demand technology to again

(Paperback)

(Paperback)

(Paperback)

In a series of three papers published in 1930 and 1931, Paley and Zygmund 44 studied a variety of problems concerning series of independent random functions and raised the question of the uniform convergence a.s. of the random Fourier series.

(Hardback)

Focuses on selection theorems that are related to the axiom of choice, particularly selectors of small Borel or Baire classes. This text constructs selectors obtained as limits of functions that are constant on the sets of certain partitions of metric spaces. It is aimed at students and researchers who wish to expand their knowledge of selectors.

(Paperback)

(Hardback)

Focuses on the difficult question of existence of Frchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. This book provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions.