▁until ▁his ▁death ▁in ▁ 1 9 9 5 . ▁For ▁the ▁academic ▁year ▁ 1 9 6 2 – 1 9 6 3 ▁Herz ▁was ▁a ▁Slo an ▁Fellow ▁at ▁Univers ité ▁de ▁Paris - S ud ▁at ▁Or say ; ▁in ▁subsequent ▁years ▁he ▁was ▁a ▁frequent ▁academic ▁visitor ▁at ▁Or say ▁for ▁a ▁month ▁or ▁two ▁each ▁year . ▁In ▁the ▁academic ▁years ▁ 1 9 5 7 - 1 9 5 8 ▁and ▁ 1 9 7 6 – 1 9 7 7 ▁he ▁was ▁a ▁visit ing ▁scholar ▁at ▁the ▁Institute ▁for ▁Advanced ▁Study . ▁Herz ▁did ▁mathematical ▁research ▁on ▁spectral ▁synth esis , ▁positive ▁definite ▁functions , ▁Fourier ▁transform s ▁on ▁convex ▁sets , ▁potential ▁theory , ▁H p , ▁and ▁B MO . ▁According ▁to ▁Nicholas ▁Var op oul os , ▁Herz ▁made ▁contributions ▁" to ▁the ▁theory ▁of ▁symmetric ▁spaces , ▁Lie ▁groups ▁and ▁the ▁heat ▁kernel ▁on ▁these ; ▁among ▁other ▁things ▁he ▁succeeded ▁in ▁class ifying ▁all ▁faithful ▁representations ▁of ▁Lie ▁groups ▁by ▁contact ▁transformations ▁of ▁a ▁compact ▁manifold ." ▁ ▁In ▁ 1 9 7 8 ▁he ▁was ▁elected ▁of ▁a ▁Fellow ▁of ▁the ▁Royal ▁Society ▁of ▁Canada . ▁In ▁ 1 9 8 6 ▁he ▁was ▁awarded ▁the ▁J ef fer y – Will iams ▁Prize ▁by ▁the ▁Canadian ▁Mathemat ical ▁Society . ▁The ▁Institut ▁des ▁sciences ▁math ém atiques ▁( a ▁cons ort ium ▁of ▁eight ▁Quebec ▁univers ities ) ▁established ▁a ▁prize ▁in ▁honour ▁of ▁Carl ▁Herz . ▁He