Asymptotic Muntz-Szasz Theorems
Jim Agler, John McCarthy
TL;DR
This paper investigates the structure of monomial spaces within , defining them as subspaces approximable by monomial function spans, and explores their properties and characteristics.
Contribution
It introduces a formal definition of monomial spaces and characterizes their structure, advancing understanding of approximation in .
Findings
Monomial spaces can be characterized by specific structural properties.
The paper establishes conditions under which subspaces are approximable by monomial functions.
It extends classical Muntz-Szasz theorems to a broader context.
Abstract
We define a monomial space to be a subspace of that can be approximated by spaces that are spanned by monomial functions. We describe the structure of monomial spaces.
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Taxonomy
TopicsAdvanced Banach Space Theory · Functional Equations Stability Results · Holomorphic and Operator Theory