Inversion of An Analytic Operator Function Through Fredholm Quotients and its Application
Abstract
Abstract We characterize the inverse of an analytic Fredholm operator-valued function A ( z ) near an isolated singularity within a general Banach space framework. Our approach relies on the sequential factorization of A ( z ) via Fredholm quotient operators. By analyzing the properties of these quotient operators near $$z=z_0$$ z = z 0 , we fully characterize the Laurent series expansion of the inverse of A ( z ) in terms of its Taylor coefficients around the singularity. These theoretical results are subsequently applied to characterize the solution of a general autoregressive law of motion in a Banach space.
Fields of Study & Subjects
Mathematical functions and polynomials
Numerical methods in inverse problems
Matrix Theory and Algorithms
Publication details
- Journal / source
- Results in Mathematics
- Publisher
- Springer Science and Business Media LLC
- Volume
- 81
- Issue
- 4
- Publication date
- 15 May 2026
- Language
- EN