Embeddings of Müntz spaces: the Hilbertian case

Details Embeddings of Müntz spaces: the Hilbertian case Embeddings of Müntz spaces: the Hilbertian case

2011-10-25

arxiv.org/abs/1110.5422v1

Mathematics

Functional Analysis

Scientific paper

Given a strictly increasing sequence $\Lambda=(\lambda_n)$ of nonegative real numbers, with $\sum_{n=1}^\infty \frac{1}{\lambda_n}<\infty$, the M\"untz spaces $M_\Lambda^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\lambda_n}$. We discuss properties of the embedding $M_\Lambda^p\subset L^p(\mu)$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$. Most of the results are obtained for the Hilbertian case $p=2$, in which we give conditions for the embedding to be bounded, compact, or to belong to the Schatten--von Neumann ideals.

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