Year: 2024
Type: article
Abstract: We study entropy numbers and box dimension of (the image of) homogeneous polynomials and holomorphic functions between Banach spaces. First, we see that entropy numbers and box dimensions of subsets of Banach spaces are related. We show that the box dimension of the image of a ball under a homogeneous polynomial is finite if and only if it spans a finite‐dimensional subspace, but this is not true for holomorphic functions. Furthermore, we relate the entropy numbers of a holomorphic function to those of the polynomials of its Taylor series expansion. As a consequence, if the box dimension of the image of a ball by a holomorphic function is finite, then the entropy numbers of the polynomials in the Taylor series expansion of at any point of the ball belong to for every .
Source: Mathematische Nachrichten
Authors: Daniel Carando, Carlos D'Andrea, Leodan A. Torres, Pablo Turco
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404872291