One-dimensional Functional Equations: Operator Theory: Advances and Applications, cartea 144

1 Implicit Functions.- 1.1 Formal solvability.- 1.2 Theorem on local solvability.- 1.3 Transformations of equations.- 1.4 Global solvability.- 1.5 Comments and references.- 2 Classification of One-dimensional Mappings.- 2.1 Wandering and non-wandering subsets.- 2.2 Mappings with wandering compact sets.- 2.3 Local structure of mappings at an isolated fixed point.- 2.4 Diffeomorphisms with isolated fixed points.- 2.5 One-dimensional flows and vector fields.- 2.6 Embedding problem and iterative roots.- 2.7 Comments and references.- 3 Generalized Abel Equation.- 3.1 Local solvability.- 3.2 Global solutions of equations with not more than one fixed point.- 3.3 Gluing method for linear equations with several fixed points.- 3.4 Comments and references.- 4 Equations with Several Transformations of Argument.- 4.1 Local solvability.- 4.2 Extension of solutions.- 4.3 Examples.- 4.4 Difference equations in Carleman classes.- 4.5 Comments and references.- 5 Linear Equations.- 5.1 Generalized linear Abel equation.- 5.2 Localization of obstacles to solvability.- 5.3 Equations with constant coefficients.- 5.4 Equation with affine transformations of argument.- 5.5 Comments and references.

Some methods are presented in a monograph for the first time: a functional parametrization of local mappings, gluing of local solutions, a decomposition method A systematic study is carried out of connections between local and global solvability of functional equations