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Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions, Sigurdur Helgason


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Автор: Sigurdur Helgason
Название:  Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions
ISBN: 9780821832110
Издательство: Mare Nostrum (Eurospan)
Классификация:




ISBN-10: 0821832115
Обложка/Формат: Paperback
Страницы: 667
Вес: 0.67 кг.
Дата издания: 30.06.2022
Серия: Mathematical surveys and monographs
Язык: English
Размер: 23.62 x 16.00 x 3.30 cm
Читательская аудитория: Professional and scholarly
Ключевые слова: Algebra,Algebraic geometry,Calculus & mathematical analysis,Geometry,Topology
Подзаголовок: Integral geometry, invariant differential operators, and spherical functions
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Поставляется из: Англии
Описание: 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.


Geometry of spherical space form groups, the

Автор: Gilkey, Peter B.
Название: Geometry of spherical space form groups, the
ISBN: 9813220783 ISBN-13(EAN): 9789813220782
Издательство: World Scientific Publishing
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Цена: 26928.00 р.
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Описание:

This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.

This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.

Hessian polyhedra, invariant theory and appell hypergeometric functions

Автор: Yang, Lei (peking Univ, China)
Название: Hessian polyhedra, invariant theory and appell hypergeometric functions
ISBN: 981320947X ISBN-13(EAN): 9789813209473
Издательство: World Scientific Publishing
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Цена: 21384.00 р.
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Описание:

Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group ����216. It provides another beautiful example on the fundamental unity of mathematics.

Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications

Автор: Karl K. Sabelfeld, Irina A. Shalimova
Название: Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications
ISBN: 3110315297 ISBN-13(EAN): 9783110315295
Издательство: Walter de Gruyter
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Цена: 27884.00 р.
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Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics

Автор: Galaktionov, Victor A. , Svirshchevskii, Sergey
Название: Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics
ISBN: 0367389975 ISBN-13(EAN): 9780367389970
Издательство: Taylor&Francis
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Цена: 9798.00 р.
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Описание:

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.

This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders.

The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.

The Geometric Hopf Invariant and Surgery Theory

Автор: Crabb
Название: The Geometric Hopf Invariant and Surgery Theory
ISBN: 3319713051 ISBN-13(EAN): 9783319713052
Издательство: Springer
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Цена: 19564.00 р.
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Описание: Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature.

Geometric invariant theory

Автор: Wallach, Nolan R.
Название: Geometric invariant theory
ISBN: 3319659057 ISBN-13(EAN): 9783319659053
Издательство: Springer
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Цена: 8384.00 р.
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Описание: Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature.

Geometric invariant theory

Автор: Mumford, David Fogarty, John Kirwan, Frances
Название: Geometric invariant theory
ISBN: 3642634001 ISBN-13(EAN): 9783642634000
Издательство: Springer
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Цена: 19564.00 р.
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Описание: This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan.

Analysis of Spherical Symmetries in Euclidean Spaces

Автор: Claus M?ller
Название: Analysis of Spherical Symmetries in Euclidean Spaces
ISBN: 0387949496 ISBN-13(EAN): 9780387949499
Издательство: Springer
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Цена: 21661.00 р.
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Описание: Offers a fresh and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. This work uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. It is particularly important for the complexification of the Funk-Hecke.

Spherical Harmonics In P Dimensions

Автор: Efthimiou Costas Et Al
Название: Spherical Harmonics In P Dimensions
ISBN: 9814596698 ISBN-13(EAN): 9789814596695
Издательство: World Scientific Publishing
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Цена: 9821.00 р.
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Описание: The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter.

Geometric Invariant Theory for Polarized Curves

Автор: Gilberto Bini; Fabio Felici; Margarida Melo; Filip
Название: Geometric Invariant Theory for Polarized Curves
ISBN: 3319113364 ISBN-13(EAN): 9783319113364
Издательство: Springer
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Цена: 4890.00 р.
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Описание:

Introduction.- Singular Curves.- Combinatorial Results.- Preliminaries on GIT.- Potential Pseudo-stability Theorem.- Stabilizer Subgroups.- Behavior at the Extremes of the Basic Inequality.- A Criterion of Stability for Tails.- Elliptic Tails and Tacnodes with a Line.- A Strati_cation of the Semistable Locus.- Semistable, Polystable and Stable Points (part I).- Stability of Elliptic Tails.- Semistable, Polystable and Stable Points (part II).- Geometric Properties of the GIT Quotient.- Extra Components of the GIT Quotient.- Compacti_cations of the Universal Jacobian.- Appendix: Positivity Properties of Balanced Line Bundles.

Spherical Radial Basis Functions, Theory and Applications

Автор: Simon Hubbert; Qu?c Th?ng Le Gia; Tanya M. Morton
Название: Spherical Radial Basis Functions, Theory and Applications
ISBN: 3319179381 ISBN-13(EAN): 9783319179384
Издательство: Springer
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Цена: 6986.00 р.
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Описание: This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere.

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration

Автор: Zamora Saiz Alfonso, Zъсiga-Rojas Ronald A.
Название: Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
ISBN: 3030678288 ISBN-13(EAN): 9783030678289
Издательство: Springer
Цена: 9083.00 р.
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Описание: Preface.- Introduction.- Preliminaries.- Geometric Invariant Theory.- Moduli Space of Vector Bundles.- Unstability Correspondence.- Stratifications on the Moduli Space of Higgs Bundles.- References.- Index.


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