δ-Universal Taylor Series
Abstract
We present a new type of universal series, termed $\delta$-universal series, for which the sum of squared coefficients satisfies $$\sum\limits_{k=0}^{\infty} |a_k|^2 < \delta$$ for an arbitrarily small $\delta > 0$. We establish a version of Seleznev's theorem within this framework. To construct such $\delta$-universal series, we develop a variation of Mergelyan's theorem.
Fields of Study & Subjects
Holomorphic and Operator Theory
Analytic and geometric function theory
Approximation Theory and Sequence Spaces
Publication details
- Journal / source
- Analysis in Theory and Applications
- Volume
- 42
- Issue
- 1
- Pages
- 1–14
- Publication date
- 10 January 2026