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Stability properties of ultraholomorphic classes of Roumieu-type defined by weight matrices
Javier Jiménez-Garrido1,2, Ignacio Miguel-Cantero2,3, Javier Sanz2,3
1Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Avda. de los Castros, s/n, 39005 Santander, Spain.
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales. Serie A, Matematicas
|April 9, 2024
Summary
This study extends stability properties for ultraholomorphic functions using weight matrices, expanding prior research to broader sectors and function classes. New results are derived for weight sequence and function controls.
Area of Science:
- Complex Analysis
- Functional Analysis
- Abstract Algebra
Background:
- Extends existing research on ultraholomorphic functions (Roumieu type) from weight sequences to weight matrices.
- Addresses limitations of prior work concerning sector width and the domain of analysis.
Purpose of the Study:
- To characterize stability properties (inverse/composition closedness) for Roumieu-type ultraholomorphic functions defined by weight matrices.
- To generalize and expand known results to arbitrary sectors on the Riemann surface of the logarithm.
Main Methods:
- Utilizes a weight matrix framework to define ultraholomorphic function classes.
- Employs the construction of characteristic functions within these classes for unrestricted sectors.
Main Results:
- Establishes inverse and composition closedness for ultraholomorphic functions defined by weight matrices.
- Transfers and extends stability results from weight sequence settings to the more general weight matrix framework.
- Obtains new stability results for growth control using weight sequences or Braun-Meise-Taylor weight functions.
Conclusions:
- The weight matrix approach provides a more general framework for studying ultraholomorphic functions.
- The construction of characteristic functions is key to extending stability properties to arbitrary sectors.
- This work offers a unified perspective on stability properties across different weight-based function classes.
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