The Selected Works of Sigurdur Helgason - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Selected Works of Sigurdur Helgason write by Sigurdur Helgason. This book was released on 2009. The Selected Works of Sigurdur Helgason available in PDF, EPUB and Kindle. Collects the articles that cover invariant differential operators, geometric properties of solutions to differential equations on symmetric spaces, double fibrations in integral geometry, spherical functions and spherical transforms, duality for symmetric spaces, representation theory, and the Fourier transform on G/K.
Differential Geometry, Lie Groups, and Symmetric Spaces
Differential Geometry, Lie Groups, and Symmetric Spaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Differential Geometry, Lie Groups, and Symmetric Spaces write by Sigurdur Helgason. This book was released on 2001-06-12. Differential Geometry, Lie Groups, and Symmetric Spaces available in PDF, EPUB and Kindle. A great book ... a necessary item in any mathematical library. --S. S. Chern, University of California A brilliant book: rigorous, tightly organized, and covering a vast amount of good mathematics. --Barrett O'Neill, University of California This is obviously a very valuable and well thought-out book on an important subject. --Andre Weil, Institute for Advanced Study The study of homogeneous spaces provides excellent insights into both differential geometry and Lie groups. In geometry, for instance, general theorems and properties will also hold for homogeneous spaces, and will usually be easier to understand and to prove in this setting. For Lie groups, a significant amount of analysis either begins with or reduces to analysis on homogeneous spaces, frequently on symmetric spaces. For many years and for many mathematicians, Sigurdur Helgason's classic Differential Geometry, Lie Groups, and Symmetric Spaces has been--and continues to be--the standard source for this material. Helgason begins with a concise, self-contained introduction to differential geometry. Next is a careful treatment of the foundations of the theory of Lie groups, presented in a manner that since 1962 has served as a model to a number of subsequent authors. This sets the stage for the introduction and study of symmetric spaces, which form the central part of the book. The text concludes with the classification of symmetric spaces by means of the Killing-Cartan classification of simple Lie algebras over $\mathbb{C}$ and Cartan's classification of simple Lie algebras over $\mathbb{R}$, following a method of Victor Kac. The excellent exposition is supplemented by extensive collections of useful exercises at the end of each chapter. All of the problems have either solutions or substantial hints, found at the back of the book. For this edition, the author has made corrections and added helpful notes and useful references. Sigurdur Helgason was awarded the Steele Prize for Differential Geometry, Lie Groups, and Symmetric Spaces and Groups and Geometric Analysis.
Integral Geometry and Radon Transforms
Integral Geometry and Radon Transforms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Integral Geometry and Radon Transforms write by Sigurdur Helgason. This book was released on 2010-11-17. Integral Geometry and Radon Transforms available in PDF, EPUB and Kindle. In this text, integral geometry deals with Radon’s problem of representing a function on a manifold in terms of its integrals over certain submanifolds—hence the term the Radon transform. Examples and far-reaching generalizations lead to fundamental problems such as: (i) injectivity, (ii) inversion formulas, (iii) support questions, (iv) applications (e.g., to tomography, partial di erential equations and group representations). For the case of the plane, the inversion theorem and the support theorem have had major applications in medicine through tomography and CAT scanning. While containing some recent research, the book is aimed at beginning graduate students for classroom use or self-study. A number of exercises point to further results with documentation. From the reviews: “Integral Geometry is a fascinating area, where numerous branches of mathematics meet together. the contents of the book is concentrated around the duality and double vibration, which is realized through the masterful treatment of a variety of examples. the book is written by an expert, who has made fundamental contributions to the area.” —Boris Rubin, Louisiana State University
Collected Papers of John Milnor
Collected Papers of John Milnor - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Collected Papers of John Milnor write by John Willard Milnor. This book was released on 1994. Collected Papers of John Milnor available in PDF, EPUB and Kindle.
Groups and Geometric Analysis
Groups and Geometric Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Groups and Geometric Analysis write by Sigurdur Helgason. This book was released on 2022-03-17. Groups and Geometric Analysis available in PDF, EPUB and Kindle. Group-theoretic methods have taken an increasingly prominent role in analysis. Some of this change has been due to the writings of Sigurdur Helgason. This book is an introduction to such methods on spaces with symmetry given by the action of a Lie group. The introductory chapter is a self-contained account of the analysis on surfaces of constant curvature. Later chapters cover general cases of the Radon transform, spherical functions, invariant operators, compact symmetric spaces and other topics. This book, together with its companion volume, Geometric Analysis on Symmetric Spaces (AMS Mathematical Surveys and Monographs series, vol. 39, 1994), has become the standard text for this approach to geometric analysis. Sigurdur Helgason was awarded the Steele Prize for outstanding mathematical exposition for Groups and Geometric Analysis and Differential Geometry, Lie Groups and Symmetric Spaces.
