A General Fredholm Theory III: Fredholm Functors and Polyfolds

Polyfolds And A General Fredholm Theory

A General Fredholm Theory I: A Splicing-Based Differential Geometry

1 Introduction In a series of papers we develop a generalized Fredholm theory and demonstrate its applicability to a variety of problems including Floer theory, Gromov-Witten theory, contact homology, and symplectic field theory. Here are some of the basic common features: • The moduli spaces are solutions of elliptic PDE's showing serious non-compactness phenomena having well-known names like ...

Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero with Applications

We develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and finite solvability of ...

Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of A-proper Maps with Applications

1. Summary. In Part I, we develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is also studied. We apply these results to the unique and...

Theory of block-pulse functions in numerical solution of Fredholm integral equations of the second ‎kind‎

Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...