Embeddings for Infinite-Dimensional Integration and $L_2$-Approximation with Increasing Smoothness
Provides theoretical error bounds for high-dimensional integration and approximation problems, relevant to numerical analysis and computational mathematics.
The paper studies integration and L2-approximation on countable tensor products of function spaces with increasing smoothness, deriving sharp upper and lower bounds for minimal errors in Korobov, Walsh, Haar, and Sobolev spaces.
We study integration and $L_2$-approximation on countable tensor products of function spaces of increasing smoothness. We obtain upper and lower bounds for the minimal errors, which are sharp in many cases including, e.g., Korobov, Walsh, Haar, and Sobolev spaces. For the proofs we derive embedding theorems between spaces of increasing smoothness and appropriate weighted function spaces of fixed smoothness.