My buddy is defending his thesis on mathematical optimization (multistage stochastic optimization problems among other things) next week. I'd like to offer him some rare, original, high quality and/or highly classical math textbook as a present.

Given that his tastes bend towards analysis (especially functional analysis) and given the nature of his research, what book would you recommend I buy?

Could be any level from junior to gradschool, but with emphasis on rigor, aesthetics in proofs and explanations, and timelessness. Think Hardy's book on number theory, but focused on analysis instead. He's French but also likes to read in English.

Pic related, one of my first ideas, Laurent Schwartz's Cours d'Analyse.