On The Foundations Of Nonlinear Generalized Functions I And Ii PDF Download
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Author | : Michael Grosser |
Publisher | : American Mathematical Soc. |
Total Pages | : 113 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : 0821827294 |
Download On the Foundations of Nonlinear Generalized Functions I and II Book in PDF, ePub and Kindle
In part 1 of this title the authors construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given.
Author | : Hebe de Azevedo Biagioni |
Publisher | : Springer |
Total Pages | : 226 |
Release | : 2006-11-14 |
Genre | : Mathematics |
ISBN | : 3540469818 |
Download A Nonlinear Theory of Generalized Functions Book in PDF, ePub and Kindle
This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.
Author | : Michael Grosser |
Publisher | : Springer Science & Business Media |
Total Pages | : 556 |
Release | : 2001-11-30 |
Genre | : Mathematics |
ISBN | : 9781402001451 |
Download Geometric Theory of Generalized Functions with Applications to General Relativity Book in PDF, ePub and Kindle
This work provides the first comprehensive introduction to the nonlinear theory of generalized functions (in the sense of Colombeau's construction) on differentiable manifolds. Particular emphasis is laid on a diffeomorphism invariant geometric approach to embedding the space of Schwartz distributions into algebras of generalized functions. The foundations of a `nonlinear distributional geometry' are developed, supplying a solid base for an increasing number of applications of algebras of generalized functions to questions of a primarily geometric mature, in particular in mathematical physics. Applications of the resulting theory to symmetry group analysis of differential equations and the theory of general relativity are presented in separate chapters. These features distinguish the present volume from earlier introductory texts and monographs on the subject. Audience: The book will be of interest to graduate students as well as to researchers in functional analysis, partial differential equations, differential geometry, and mathematical physics.
Author | : Hebe Azevedo Biagioni |
Publisher | : |
Total Pages | : 228 |
Release | : 1988 |
Genre | : Nonlinear theories |
ISBN | : |
Download Introduction to a Nonlinear Theory of Generalized Functions Book in PDF, ePub and Kindle
Author | : Hebe Azevedo Biagioni |
Publisher | : Springer |
Total Pages | : 704 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download A Nonlinear Theory of Generalized Functions Book in PDF, ePub and Kindle
Author | : Pierre Lochak |
Publisher | : American Mathematical Soc. |
Total Pages | : 162 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821832689 |
Download On the Splitting of Invariant Manifolds in Multidimensional Near-Integrable Hamiltonian Systems Book in PDF, ePub and Kindle
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Author | : Kai Behrend |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821829297 |
Download Derived $\ell $-Adic Categories for Algebraic Stacks Book in PDF, ePub and Kindle
This text is intended for graduate students and research mathematicians interested in algebraic geometry, category theory and homological algebra.
Author | : Jürgen Ritter |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829289 |
Download The Lifted Root Number Conjecture and Iwasawa Theory Book in PDF, ePub and Kindle
This paper concerns the relation between the Lifted Root Number Conjecture, as introduced in [GRW2], and a new equivariant form of Iwasawa theory. A main conjecture of equivariant Iwasawa theory is formulated, and its equivalence to the Lifted Root Number Conjecture is shown subject to the validity of a semi-local version of the Root Number Conjecture, which itself is proved in the case of a tame extension of real abelian fields.
Author | : M. A. Mandell |
Publisher | : American Mathematical Soc. |
Total Pages | : 125 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082182936X |
Download Equivariant Orthogonal Spectra and $S$-Modules Book in PDF, ePub and Kindle
The last few years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993. The most well-known examples are the category of $S$-modules and the category of symmetric spectra. We focus on the category of orthogonal spectra, which enjoys some of the best features of $S$-modules and symmetric spectra and which is particularly well-suited to equivariant generalization. We first complete the nonequivariant theory by comparing orthogonal spectra to $S$-modules. We then develop the equivariant theory.For a compact Lie group $G$, we construct a symmetric monoidal model category of orthogonal $G$-spectra whose homotopy category is equivalent to the classical stable homotopy category of $G$-spectra. We also complete the theory of $S_G$-modules and compare the categories of orthogonal $G$-spectra and $S_G$-modules. A key feature is the analysis of change of universe, change of group, fixed point, and orbit functors in these two highly structured categories for the study of equivariant stable homotopy theory.
Author | : Ethan Akin |
Publisher | : American Mathematical Soc. |
Total Pages | : 146 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833383 |
Download Dynamics of Topologically Generic Homeomorphisms Book in PDF, ePub and Kindle
The goal of this work is to describe the dynamics of generic homeomorphisms of certain compact metric spaces $X$. Here ``generic'' is used in the topological sense -- a property of homeomorphisms on $X$ is generic if the set of homeomorphisms with the property contains a residual subset (in the sense of Baire category) of the space of all homeomorphisms on $X$. The spaces $X$ we consider are those with enough local homogeneity to allow certain localized perturbations of homeomorphisms; for example, any compact manifold is such a space. We show that the dynamics of a generic homeomorphism is quite complicated, with a number of distinct dynamical behaviors coexisting (some resemble subshifts of finite type, others, which we call `generalized adding machines', appear strictly periodic when viewed to any finite precision, but are not actually periodic). Such a homeomorphism has infinitely many, intricately nested attractors and repellors, and uncountably many distinct dynamically-connected components of the chain recurrent set. We single out several types of these ``chain components'', and show that each type occurs densely (in an appropriate sense) in the chain recurrent set. We also identify one type that occurs generically in the chain recurrent set. We also show that, at least for $X$ a manifold, the chain recurrent set of a generic homeomorphism is a Cantor set, so its complement is open and dense. Somewhat surprisingly, there is a residual subset of $X$ consisting of points whose limit sets are chain components of a type other than the type of chain components that are residual in the space of all chain components. In fact, for each generic homeomorphism on $X$ there is a residual subset of points of $X$ satisfying a stability condition stronger than Lyapunov stability.