Spherical Inversion On Sln

Author : Jay Jorgenson,Serge Lang
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493023

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Spherical Inversion on SLn(R) by Jay Jorgenson,Serge Lang Pdf

For the most part the authors are concerned with SLn(R) and with invariant differential operators, the invarinace being with respect to various subgroups. To a large extent, this book carries out the general results of Harish-Chandra.

Author : Jay Jorgenson,Serge Lang
Publisher : Unknown
Page : 448 pages
File Size : 45,6 Mb
Release : 2001-06-21
Category : Electronic
ISBN : 1468493035

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Spherical Inversion on Sln by Jay Jorgenson,Serge Lang Pdf

Author : Jay Jorgenson,Serge Lang
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 49,7 Mb
Release : 2009-02-20
Category : Mathematics
ISBN : 9780387380322

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The Heat Kernel and Theta Inversion on SL2(C) by Jay Jorgenson,Serge Lang Pdf

The worthy purpose of this text is to provide a complete, self-contained development of the trace formula and theta inversion formula for SL(2,Z[i])\SL(2,C). Unlike other treatments of the theory, the approach taken here is to begin with the heat kernel on SL(2,C) associated to the invariant Laplacian, which is derived using spherical inversion. The heat kernel on the quotient space SL(2,Z[i])\SL(2,C) is arrived at through periodization, and further expanded in an eigenfunction expansion. A theta inversion formula is obtained by studying the trace of the heat kernel. Following the author's previous work, the inversion formula then leads to zeta functions through the Gauss transform./

Author : Pascal Auscher,T. Coulhon,Alexander Grigoryan
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 55,9 Mb
Release : 2003
Category : Elliptic operators
ISBN : 9780821833834

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Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces by Pascal Auscher,T. Coulhon,Alexander Grigoryan Pdf

This volume contains the expanded lecture notes of courses taught at the Emile Borel Centre of the Henri Poincare Institute (Paris). In the book, leading experts introduce recent research in their fields. The unifying theme is the study of heat kernels in various situations using related geometric and analytic tools. Topics include analysis of complex-coefficient elliptic operators, diffusions on fractals and on infinite-dimensional groups, heat kernel and isoperimetry on Riemannian manifolds, heat kernels and infinite dimensional analysis, diffusions and Sobolev-type spaces on metric spaces, quasi-regular mappings and $p$-Laplace operators, heat kernel and spherical inversion on $SL 2(C)$, random walks and spectral geometry on crystal lattices, isoperimetric and isocapacitary inequalities, and generating function techniques for random walks on graphs. This volume is suitable for graduate students and research mathematicians interested in random processes and analysis on manifolds.

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 923 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300410

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Algebra by Serge Lang Pdf

This book is intended as a basic text for a one year course in algebra at the graduate level or as a useful reference for mathematicians and professionals who use higher-level algebra. This book successfully addresses all of the basic concepts of algebra. For the new edition, the author has added exercises and made numerous corrections to the text. From MathSciNet's review of the first edition: "The author has an impressive knack for presenting the important and interesting ideas of algebra in just the "right" way, and he never gets bogged down in the dry formalism which pervades some parts of algebra."

Author : Frank Nielsen
Publisher : Springer
Page : 392 pages
File Size : 40,7 Mb
Release : 2018-11-19
Category : Technology & Engineering
ISBN : 9783030025205

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Geometric Structures of Information by Frank Nielsen Pdf

This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

Author : Friedrich Ischebeck,Ravi A. Rao
Publisher : Springer Science & Business Media
Page : 339 pages
File Size : 48,7 Mb
Release : 2005-11-22
Category : Mathematics
ISBN : 9783540263708

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Ideals and Reality by Friedrich Ischebeck,Ravi A. Rao Pdf

Besides giving an introduction to Commutative Algebra - the theory of c- mutative rings - this book is devoted to the study of projective modules and the minimal number of generators of modules and ideals. The notion of a module over a ring R is a generalization of that of a vector space over a field k. The axioms are identical. But whereas every vector space possesses a basis, a module need not always have one. Modules possessing a basis are called free. So a finitely generated free R-module is of the form Rn for some n E IN, equipped with the usual operations. A module is called p- jective, iff it is a direct summand of a free one. Especially a finitely generated R-module P is projective iff there is an R-module Q with P @ Q S Rn for some n. Remarkably enough there do exist nonfree projective modules. Even there are nonfree P such that P @ Rm S Rn for some m and n. Modules P having the latter property are called stably free. On the other hand there are many rings, all of whose projective modules are free, e. g. local rings and principal ideal domains. (A commutative ring is called local iff it has exactly one maximal ideal. ) For two decades it was a challenging problem whether every projective module over the polynomial ring k[X1,. . .

Author : A.D. Alexandrov
Publisher : Springer Science & Business Media
Page : 545 pages
File Size : 45,7 Mb
Release : 2005-12-08
Category : Mathematics
ISBN : 9783540263401

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Convex Polyhedra by A.D. Alexandrov Pdf

This classic geometry text explores the theory of 3-dimensional convex polyhedra in a unique fashion, with exceptional detail. Vital and clearly written, the book includes the basics of convex polyhedra and collects the most general existence theorems for convex polyhedra that are proved by a new and unified method. This edition includes a comprehensive bibliography by V.A. Zalgaller, and related papers as supplements to the original text.

Author : Helmut Koch
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 40,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662049679

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Galois Theory of p-Extensions by Helmut Koch Pdf

Helmut Koch's classic is now available in English. Competently translated by Franz Lemmermeyer, it introduces the theory of pro-p groups and their cohomology. The book contains a postscript on the recent development of the field written by H. Koch and F. Lemmermeyer, along with many additional recent references.

Author : David E. Edmunds,William D. Evans
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 49,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662077313

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Hardy Operators, Function Spaces and Embeddings by David E. Edmunds,William D. Evans Pdf

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

Author : Sergei I. Gelfand,Yuri I. Manin
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 43,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662124925

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Methods of Homological Algebra by Sergei I. Gelfand,Yuri I. Manin Pdf

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas of derived categories and derived functors. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 168 pages
File Size : 50,9 Mb
Release : 2002-11-25
Category : Mathematics
ISBN : 3540442375

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Trees by Jean-Pierre Serre Pdf

The seminal ideas of this book played a key role in the development of group theory since the 70s. Several generations of mathematicians learned geometric ideas in group theory from this book. In it, the author proves the fundamental theorem for the special cases of free groups and tree products before dealing with the proof of the general case. This new edition is ideal for graduate students and researchers in algebra, geometry and topology.

Author : Georges Gras
Publisher : Springer Science & Business Media
Page : 513 pages
File Size : 44,6 Mb
Release : 2005-02-16
Category : Mathematics
ISBN : 9783540441335

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Class Field Theory by Georges Gras Pdf

Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.

Author : Vladimir Kanovei,Michael Reeken
Publisher : Springer Science & Business Media
Page : 421 pages
File Size : 47,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662089989

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Nonstandard Analysis, Axiomatically by Vladimir Kanovei,Michael Reeken Pdf

In the aftermath of the discoveries in foundations of mathematiC's there was surprisingly little effect on mathematics as a whole. If one looks at stan dard textbooks in different mathematical disciplines, especially those closer to what is referred to as applied mathematics, there is little trace of those developments outside of mathematical logic and model theory. But it seems fair to say that there is a widespread conviction that the principles embodied in the Zermelo - Fraenkel theory with Choice (ZFC) are a correct description of the set theoretic underpinnings of mathematics. In most textbooks of the kind referred to above, there is, of course, no discussion of these matters, and set theory is assumed informally, although more advanced principles like Choice or sometimes Replacement are often mentioned explicitly. This implicitly fixes a point of view of the mathemat ical universe which is at odds with the results in foundations. For example most mathematicians still take it for granted that the real number system is uniquely determined up to isomorphism, which is a correct point of view as long as one does not accept to look at "unnatural" interpretations of the membership relation.

Author : Grigorii A. Margulis
Publisher : Springer Science & Business Media
Page : 144 pages
File Size : 53,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662090701

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On Some Aspects of the Theory of Anosov Systems by Grigorii A. Margulis Pdf

The seminal 1970 Moscow thesis of Grigoriy A. Margulis, published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature. The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.