▁the ▁Mathemat ics ▁Research ▁Center ▁at ▁the ▁University ▁of ▁Wisconsin – Mad ison , ▁from ▁ 1 9 8 4 ▁to ▁ 1 9 9 0 ▁as ▁H ille - Pro f essor ▁of ▁Mathemat ics . ▁From ▁ 1 9 8 8 ▁until ▁his ▁ret irement ▁he ▁was ▁a ▁professor ▁at ▁the ▁University ▁of ▁California , ▁Santa ▁Barbara . ▁Cr and all ▁was ▁several ▁times ▁a ▁visit ing ▁professor ▁at ▁the ▁University ▁of ▁Paris , ▁where ▁he ▁received ▁an ▁honor ary ▁doctor ate ▁in ▁ 1 9 9 9 . ▁His ▁legacy ▁of ▁contributions ▁contains ▁all ▁but ▁not ▁limited ▁to : ▁Ban ach ▁solutions ▁in ▁E uclidean ▁spaces , ▁Fourier ▁transform s ▁of ▁plan ar ▁variables , ▁P DE ▁concepts ▁and ▁iterations ▁for ▁sequence ▁analysis , ▁sem igr oup ▁transform ▁solutions , ▁differential ▁harm onic ▁study ▁of ▁diver gent ▁hyper bo le , ▁physical ▁transformations ▁of ▁finite ▁Jacob ian ▁entities , ▁unique ▁harm onic ▁populations ▁in ▁conver gent ▁context s , ▁application ▁of ▁abstract ▁existence ▁principles ▁on ▁non - linear ▁context s , ▁normal ized ▁vector ▁sequ encing ▁in ▁multi - dimensional ▁par alla x ▁geomet ries , ▁and ▁the ▁mathematical ▁equivalence ▁study ▁of ▁top ographical ▁dis similar ▁nodes ▁using ▁traditional ▁non - linear ▁sur f acing ▁theories ▁to ▁produce ▁distinct ▁solutions ▁in ▁the ▁real m ▁of ▁differential ▁multi - variable ▁applications . ▁ ▁Cr and all ▁works ▁primarily ▁on ▁partial ▁differential ▁equations , ▁e . g ., ▁with ▁b if ur cation ▁theory , ▁evolution ▁equations , ▁generation ▁of ▁sem igr