overlap of function spaces

Overlap of function spaces refers to situations where a function belongs to more than one mathematical space characterized by certain properties, such as smoothness or integrability. Think of it like a person fitting into multiple groups based on different criteria: for example, someone might be both a marathon runner and a cyclist. In mathematics, these overlaps reveal how different sets of functions share common members, helping us understand and analyze complex behaviors, like signals or solutions to equations, within multiple frameworks simultaneously. This overlap simplifies studying functions that meet multiple criteria at once.