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Degree Theory for Equivariant Maps, the General $S^1$-Action
In this paper, we consider general [italic]S1-actions, which may differ on the domain and on the range, with isotropy subspaces with one dimension more on the domain. In the special case of self-maps the [italic]S1-degree is given by the usual degree of the invariant part, while for one parameter [italic]S1-maps one has an integer for each isotropy subgroup different from [italic]S1. In particular we recover all the [italic]S1-degrees introduced in special cases by other authors and we are also able to interpret period doubling results on the basis of our [italic]S1-degree. The applications concern essentially periodic solutions of ordinary differential equations.
Recent Trends in Nonlinear Analysis
The book contains a collection of 21 original research papers which report on recent developments in various fields of nonlinear analysis. The collection covers a large variety of topics ranging from abstract fields such as algebraic topology, functional analysis, operator theory, spectral theory, analysis on manifolds, partial differential equations, boundary value problems, geometry of Banach spaces, measure theory, variational calculus, and integral equations, to more application-oriented fields like control theory, numerical analysis, mathematical physics, mathematical economy, and financial mathematics. The book is addressed to all specialists interested in nonlinear functional analysis and its applications, but also to postgraduate students who want to get in touch with this important field of modern analysis. It is dedicated to Alfonso Vignoli who has essentially contributed to the field, on the occasion of his sixtieth birthday.
Mathematical and Statistical Methods for Actuarial Sciences and Finance
The cooperation and contamination between mathematicians, statisticians and econometricians working in actuarial sciences and finance is improving the research on these topics and producing numerous meaningful scientific results. This volume presents new ideas, in the form of four- to six-page papers, presented at the International Conference eMAF2020 – Mathematical and Statistical Methods for Actuarial Sciences and Finance. Due to the now sadly famous COVID-19 pandemic, the conference was held remotely through the Zoom platform offered by the Department of Economics of the Ca’ Foscari University of Venice on September 18, 22 and 25, 2020. eMAF2020 is the ninth edition of an internationa...
Nonlinear Functional Analysis and Its Applications
A NATO Advanced Study Institute on Nonlinear Functional Analysis and Its Applications was held in Hotel Villa del Mare, Maratea, It.a1y during April 22 - May 3, 1985. This volume consists of the Proceedings of the Institute. These Proceedings include the invited lectures and contributed papers given during the Institute. The papers have been refereed. The aim of these lectures was to bring together recent and up-to-date development of the subject, and to give directions for future research. The main topics covered include: degree and generalized degree theory, results related to Hamiltonian Systems, Fixed Point theory, linear and nonlinear Differential and Partial Differential Equations, Theory of Nielsen Numbers, and applications to Dynamical Systems, Bifurcation Theory, Hamiltonian Systems, Minimax Theory, Heat Equations, Pendulum Equation, Nonlinear Boundary Value Problems, and Dirichlet and Neumann problems for elliptic equations and the periodic Dirichlet problem for semilinear beam equations. I express my sincere thanks to Professors F. E. Browder, R. Conti, A. Do1d, D. E. Edmunds and J. Mawhin members of the Advisory Committee.
Mapping Degree Theory
This textbook treats the classical parts of mapping degree theory, with a detailed account of its history traced back to the first half of the 18th century. After a historical first chapter, the remaining four chapters develop the mathematics. An effort is made to use only elementary methods, resulting in a self-contained presentation. Even so, the book arrives at some truly outstanding theorems: the classification of homotopy classes for spheres and the Poincare-Hopf Index Theorem, as well as the proofs of the original formulations by Cauchy, Poincare, and others. Although the mapping degree theory you will discover in this book is a classical subject, the treatment is refreshing for its si...
Orientation and the Leray-Schauder Theory for Fully Nonlinear Elliptic Boundary Value Problems
The aim of this work is to develop an additive, integer-valued degree theory for the class of quasilinear Fredholm mappings. This class is sufficiently large that, within its framework, one can study general fully nonlinear elliptic boundary value problems. A degree for the whole class of quasilinear Fredholm mappings must necessarily accommodate sign-switching of the degree along admissible homotopies. The authors introduce ''parity'', a homotopy invariant of paths of linear Fredholm operators having invertible endpoints. The parity provides a complete description of the possible changes in sign of the degree and thereby permits use of the degree to prove multiplicity and bifurcation theorems for quasilinear Fredholm mappings. Applications are given to the study of fully nonlinear elliptic boundary value problems.
Weak Type Estimates for Cesaro Sums of Jacobi Polynomial Series
This work completely characterizes the behaviour of Cesaro means of any order of the Jacobi polynomials. In particular, pointwise estimates are derived for the Cesaro mean kernel. Complete answers are given for the convergence almost everywhere of partial sums of Cesaro means of functions belonging to the critical L ]p spaces. This characterization is deduced from weak type estimates for the maximal partial sum operator. The methods used are fairly general and should apply to other series of special functions.
Continuous Images of Arcs and Inverse Limit Methods
Continuous images of ordered continua are investigated. The paper gives various properties of their monotone images and inverse limits of their inverse systems (or sequences) with monotone bonding surjections. Some factorization theorems are provided. Special attention is given to one-dimensional spaces which are continuous images of arcs and, among them, various classes of rim-finite continua. The methods of proofs include cyclic element theory, T-set approximations and null-family decompositions. The paper brings also new properties of cyclic elements and T-sets in locally connected continua, in general.
Associated Graded Algebra of a Gorenstein Artin Algebra
In 1904, Macaulay described the Hilbert function of the intersection of two plane curve branches: It is the sum of a sequence of functions of simple form. This monograph describes the structure of the tangent cone of the intersection underlying this symmetry. Iarrobino generalizes Macaulay's result beyond complete intersections in two variables to Gorenstein Artin algebras in an arbitrary number of variables. He shows that the tangent cone of a Gorenstein singularity contains a sequence of ideals whose successive quotients are reflexive modules. Applications are given to determining the multiplicity and orders of generators of Gorenstein ideals and to problems of deforming singular mapping germs. Also included are a survey of results concerning the Hilbert function of Gorenstein Artin algebras and an extensive bibliography.
Symplectic Cobordism and the Computation of Stable Stems
This memoir consists of two independent papers. In the first, "The symplectic cobordism ring III" the classical Adams spectral sequence is used to study the symplectic cobordism ring [capital Greek]Omega[superscript]* [over] [subscript italic capital]S[subscript italic]p. In the second, "The symplectic Adams Novikov spectral sequence for spheres" we analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres.
