His work with Ramanujan begat probabilistic number theory. His work on Tauberian theorems and divergent series has probabilistic proofs and interpretations. Finally, Hardy spaces are a central ingredient in stochastic calculus. This paper reviews his prejudices and accomplishments, through these examples....
1729 is the Hardy–Ramanujan number, named after a famous anecdote of the British mathematician G. H. Hardy regarding a visit to the hospital in about 1919 to see the Indian mathematician Srinivasa Ramanujan. In Hardy's words: I remember once going to see him when he was ill at Putney. ...
Relying on number theory techniques we exhibit some examples which do not provide superposition operators. We finally look at the action of the differentiation and integration operators on these spaces. This is a preview of subscription content, log in via an institution to check access. Similar ...