A topological splitting of the space of meromorphic germs in several variables and continuous evaluators

We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the resulting holomorphic projection at zero gives rise to a continuous evaluator (at zero) on the space of m...

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Bibliographic Details
Published in:Complex analysis and its synergies Vol. 10; no. 1
Main Authors: Dahmen, Rafael, Paycha, Sylvie, Schmeding, Alexander
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2024
Subjects:
Algebraic Geometry
Analysis
Dynamical Systems and Ergodic Theory
Functional Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Partial Differential Equations
Germs of meromorphic functions
32A20
Silva space
46E50
Evaluators
Minimal subtraction scheme
Linear pole
32A70 (Primary)
Polar germ
Meromorphic functions in several variables
81T15 (Secondary)
ISSN:2524-7581, 2197-120X
Online Access:Get full text
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Summary:We prove a topological decomposition of the space of meromorphic germs at zero in several variables with prescribed linear poles as a sum of spaces of holomorphic and polar germs. Evaluating the resulting holomorphic projection at zero gives rise to a continuous evaluator (at zero) on the space of meromorphic germs in several variables. Our constructions are carried out in the framework of Silva spaces and use an inner product on the underlying space of variables. They generalise to several variables, the topological direct decomposition of meromorphic germs at zero as sums of holomorphic and polar germs previously derived by the first and third author and provide a topological refinement of a known algebraic decomposition of such spaces previously derived by the second author and collaborators.
ISSN:2524-7581
2197-120X
DOI:10.1007/s40627-023-00130-w