Understanding the Bitcoin White Paper's Notion of "Signing" and "Verifying"
Yes. It means "sign" and "verify" exactly as in a public key system such as RSA. Bitcoin doesn't introduce new cryptographic primitives or notions; it simply combines existing ones in a novel way. So you would simply use a public key system such as RSA to implement those operations in Bitcoin. The actual algorithm used is ECDSA, but this predates Bitcoin by quite a while. Arguably the "break-through" in Bitcoin is a clever mix of existing cryptographic techniques and aligning incentives.

Another clever aspect is that Bitcoin solves a different problem than what cryptographers traditionally viewed as "digital cash". That is, Bitcoin doesn't meet all the desiderata that one would hope "digital cash" would have, but clearly it's a pretty effective solution to the colloquial meaning of "digital cash".