This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.
This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type ...
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives special emphasis to group extensions, including a detailed discussion of the Euclidean group, the oscillator group, the Bott-Virasoro group and other groups of matrices. The volume also provides ample background theory on symplectic reduction and cotangent bundle reduction.
This volume provides a detailed account of the theory of symplectic reduction by stages, along with numerous illustrations of the theory. It gives ...
This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.
This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution f...
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrodinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) Geometric properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the...
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. T...
Littlewood-Paley theory extends some of the benefits of orthogonality to situations where it doesn t make sense by letting certain oscillatory infinite series of functions be controlled in terms of infinite series of non-negative functions. Beginning in the 1980s, it was discovered that this control could be made much sharper. This book offers a gentle, well-motivated introduction to those discoveries, the methods behind them, their consequences, and some of their applications."
Littlewood-Paley theory extends some of the benefits of orthogonality to situations where it doesn t make sense by letting certain oscillatory infi...
Thestudyofthesubgroupgrowthofin?nitegroupsisanareaofmathematical research that has grown rapidly since its inception at the Groups St. Andrews conferencein1985.Ithasbecomearichtheoryrequiringtoolsfromandhaving applications to many areas of group theory. Indeed, much of this progress is chronicled by Lubotzky and Segal within their book 42]. However, one area within this study has grown explosively in the last few years. This is the study of the zeta functions of groups with polynomial s- groupgrowth, inparticularfortorsion-free?nitely-generatednilpotentgroups. These zeta functions were...
Thestudyofthesubgroupgrowthofin?nitegroupsisanareaofmathematical research that has grown rapidly since its inception at the Groups St. Andrews confere...
The main theme of this book is the stability of nonautonomous di?erential equations, with emphasis on the study of the existence and smoothness of invariant manifolds, and the Lyapunov stability of solutions. We always c- sider a nonuniform exponential behavior of the linear variational equations, given by the existence of a nonuniform exponential contraction or a nonu- form exponential dichotomy. Thus, the results hold for a much larger class of systems than in the "classical" theory of exponential dichotomies. Thedeparturepointofthebookisourjointworkontheconstructionof- variant manifolds...
The main theme of this book is the stability of nonautonomous di?erential equations, with emphasis on the study of the existence and smoothness of inv...
A classical problem in the calculus of variations is the investigation of critical points of functionals {cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {cal L} and the underlying space V does {cal L} have at most one critical point?
A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry," i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {cal L}. The "method of transformation groups" is applied to...
A classical problem in the calculus of variations is the investigation of critical points of functionals {cal L} on normed spaces V. The p...
Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a graduate background in probability theory and statistics. It will be useful to any reader wondering why it may be a good idea, to use as is often done in practice a notoriously "wrong'' (i.e. over-simplified) model to predict, estimate or classify. This point of view takes its roots in three fields: information theory, statistical mechanics, and PAC-Bayesian theorems. Results on the large deviations of trajectories of Markov chains with rare...
Statistical learning theory is aimed at analyzing complex data with necessarily approximate models. This book is intended for an audience with a gr...
When I started giving talks on regularity theory for degenerate and sin- lar parabolic equations, a ?xed-point in the conversation during the co?- break that usually followed the seminar was the apparent contrast between the beauty of the subject and its technical di?culty. I could not agree more on the beauty part but, most of the times, overwhelmingly failed to convince my audience that the technicalities were not all that hard to follow. As in many other instances, it was the fact that the results in the literature were eventually stated and proved in their most possible generality that...
When I started giving talks on regularity theory for degenerate and sin- lar parabolic equations, a ?xed-point in the conversation during the co?- bre...
