Abstract: Kernel methods are among the most popular techniques in machine learning. From a regularization theory perspective, they provide a natural choice for the hypotheses space and the ...

If the space of all real-valued functions of bounded variation on a real closed interval is endowed with the topology of simple convergence, then every bounded subset which is bounded for the values ...

Let $X$ be a Banach space with dual $X^\ast$ and let $(\Omega, \Sigma, \mu)$ be a finite measure space. Suppose $f: \Omega \rightarrow X$ is weakly measurable. There ...

Abstract: To address the issue that the ordering of sample indicators may affect the results of the grey relational analysis model (GRA) based on panel data, a novel GRA model based on vector-valued ...

Banach spaces, as complete normed vector spaces, provide a fundamental setting in modern analysis, allowing for a rigorous treatment of convergence and stability in infinite dimensions. Integrability ...

Suppose I have a vector-valued function f(x) = y, where x and y are both vectors of some length (same or different length). f could be evaluated over a regular grid of x values, producing a set of y ...

Apologies if I have missed a change, but I have been trying to run some scripts on a new firedrake build and (as well as reactivating github actions with the latest firedrake...) it seems like ...