Annals of Mathematics Studies book series

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Knot Groups ​

(Annals of Mathematics Studies, No. 56)​

By Lee Paul Neuwirth





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  • Publisher: Princeton University Press




    Number Of Pages: 113




    Publication Date: 1965-03-01





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  • Binding: Paperback


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هى سلسلة كتب كبيره غير مرتبه سوف اضيف معظمها ان شاء الله ​
 



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Harmonic Analysis in Phase Space​

(Annals of Mathematics Studies)​

By Gerald B. Folland​



  • Publisher: Princeton Univ Pr

    Number Of Pages: 288 ​


    Publication Date: 1989-03
  • Binding: Hardcover ​
Product Description


This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.​


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Triangulated Categories​


AM-148​



(Annals of Mathematics Studies)​

By Amnon Neeman​


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  • Publisher: Princeton University Press
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  • Number Of Pages: 449
  • Publication Date: 2001-02-01 ​
  • Binding: Paperback ​
Product Description



The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.​



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An Introduction to G-Functions ​

(Annals of Mathematics Studies)​

By Bernard M. Dwork, Giovanni Gerotto, Francis J. Sullivan​





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  • Publisher: Princeton Univ Pr ​
  • Number Of Pages: 246 ​
  • Publication Date: 1994-04 ​
  • Binding: Hardcover ​
Product Description


Written for advanced undergraduate and first-year graduate students, this book aims to introduce students to a serious level of p-adic analysis with important implications for number theory. The main object is the study of G-series, that is, power series y=aij=0 Ajxj with coefficients in an algebraic number field K. These series satisfy a linear differential equation Ly=0 with LIK(x) [d/dx] and have non- zero radii of convergence for each imbedding of K into the complex numbers. They have the further property that the common denominators of the first s coefficients go to infinity geometrically with the index s. After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, Andr, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G- series is again a G-series. This book will be indispensable for those wishing to study the work of Bombieri and Andr on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.​

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Functional Operators​

Volume 1​

( Measures and Integrals) (AM-21) ​

(Annals of Mathematics Studies)​

By John von Neumann​


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  • Publisher: Princeton University Press

    Number Of Pages: 272

    Publication Date: 1950-01-01 ​
  • Binding: Paperback ​
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Functional Operators
Volume 2​

The Geometry of Orthogonal Spaces ​

(AM-22) ​

(Annals of Mathematics Studies)​

By John von Neumann​


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  • Publisher: Princeton University Press
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  • Number Of Pages: 116 ​
  • Publication Date: 1950-12-31 ​
  • Binding: Paperback ​
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Spherical CR Geometry and Dehn Surgery
(AM-165) ​

(Annals of Mathematics Studies)​



By Richard Evan Schwartz​




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  • Publisher: Princeton University Press

    Number Of Pages: 200

    Publication Date: 2007-01-29 ​
  • Binding: Paperback ​
Product Description​




This book proves an analogue of William Thurston's celebrated hyperbolic Dehn surgery theorem in the context of complex hyperbolic discrete groups, and then derives two main geometric consequences from it. The first is the construction of large numbers of closed real hyperbolic 3-manifolds which bound complex hyperbolic orbifolds--the only known examples of closed manifolds that simultaneously have these two kinds of geometric structures. The second is a complete understanding of the structure of complex hyperbolic reflection triangle groups in cases where the angle is small. In an accessible and straightforward manner, Richard Evan Schwartz also presents a large amount of useful information on complex hyperbolic geometry and discrete groups.
Schwartz relies on elementary proofs and avoids quotations of preexisting technical material as much as possible. For this reason, this book will benefit graduate students seeking entry into this emerging area of research, as well as researchers in allied fields such as Kleinian groups and CR geometry.​




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Algebraic Theory of Numbers ​

(Annals of Mathematics Studies)​


By Herman Weyl​



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  • Publisher: Princeton University Press
  • Number Of Pages: 240 ​
  • Publication Date: 1954-06 ​
  • Binding: Paperback ​
Product Description​


In this, one of the first books to appear in English on the theory of numbers, the eminent mathematician Hermann Weyl explores fundamental concepts in arithmetic. The book begins with the definitions and properties of algebraic fields, which are relied upon throughout. The theory of divisibility is then discussed, from an axiomatic viewpoint, rather than by the use of ideals. There follows an introduction to ^Ip^N-adic numbers and their uses, which are so important in modern number theory, and the book culminates with an extensive examination of algebraic number fields. Weyl's own modest hope, that the work "will be of some use," has more than been fulfilled, for the book's clarity, succinctness, and importance rank it as a masterpiece of mathematical exposition.​

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Foundational Essays on
Topological Manifolds, Smoothings, and Triangulations
(AM-88)
(Annals of Mathematics Studies)
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By Robion C. Kirby, Laurence C. Siebenmann​



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  • Publisher: Princeton University Press

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  • Number Of Pages: 368
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  • Publication Date: 1977-05-01 ​
  • Binding: Paperback ​
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Moments, Monodromy, and Perversity
(AM-159)​

A Diophantine Perspective​

(Annals of Mathematics Studies)​


By Nicholas M. Katz​


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  • Publisher: Princeton University Press
  • Number Of Pages: 448 ​
  • Publication Date: 2005-09-12 ​
  • Binding: Paperback ​
Product Description​

It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family.
Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields.​


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The Hypoelliptic Laplacian
and Ray-Singer Metrics
(AM-167)
(Annals of Mathematics Studies)​


By Jean-Michel Bismut, Gilles Lebeau​




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  • Publisher: Princeton University Press

    Number Of Pages: 376

    Publication Date: 2008-09-07 ​
  • Binding: Hardcover ​
Product Description​



This book presents the analytic foundations to the theory of the hypoelliptic Laplacian. The hypoelliptic Laplacian, a second-order operator acting on the cotangent bundle of a compact manifold, is supposed to interpolate between the classical Laplacian and the geodesic flow. Jean-Michel Bismut and Gilles Lebeau establish the basic functional analytic properties of this operator, which is also studied from the perspective of local index theory and analytic torsion.
The book shows that the hypoelliptic Laplacian provides a geometric version of the Fokker-Planck equations. The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained.
The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.​


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