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2 Recll R dul given by Rg Sn To < X compute g g > SCT g > gn /o± 0 sn HO Srn i dh do Xglo o ESCZ s SCR 9 Y gctso dh ds DO R g dy gc o pns HoE@dO gcy dy Eoyy where Theree We &R R compre X n o t Y R integrte iover cqs integrte line ll ll over ll g CAT Prsevl S g znr ^ 1st relti 5 Wls des v 0 run oo R ^ i lines o gn 910 s TK RAH F Ssn o o dds d w P+jg sn s Sirglo d & 59^109 nh 5412 R g gn test tsd E µ w Rd through lesh n plnes plne n By integrtes points ^ g R p± 5h gt X while through Pr points integrte overll o similrly 0 R Eo projecti G wkod0 oo o WKO For secd ggn ggg e E integrl sn co 9tg P G GYETHSDW lt n ME si o idwk0 du W e + Th completes tsltnds pro Dg
3 i rt Eo ] Note The computti gms incorrect ound mtke in versi lemm 1 ws invoking which should be let n µgly7dhydo s 4 n ll gl d insted e glo ] Tht Net For FESCR We csider norml r R P R Rkt gn Rlo 07 n dity JOlYtMdtFt lemm S 21 / µ ly + YT dy 1521 µiy~lg dy 1521 F X Xc gn X O Eo DO + SO dsdo line through gn snhootidctsods Eotso ds directi sn in pl LTin?Tns 2 sn o tso dsdo PT z n ty lyltndg llr
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5 Given n snieioi01opt@jyogdcszltengnieio001gnt4rjncoo tz nsn C R o ln R dt s R cs zt n&r in r For X d AtTtrneiwslsHls7d5ew@JnsnFysnoeimiyFCndnlEhtFnysnioseib1yltCXYCpdydOlcyCEosD so 4 bn X 1 X t 1 X Qeo X R± we set 20 ztl in R tnr n2 where R h R 1qk g sgn oky TemperedDtributioTDe_ nd unctil Sr spce r csts ll liner ctinuous e i stying rn lc Ed < deine s some q > o T 9 < y > i 94 d ll SETCR R
6 Wek Fourier Slt t Sit t Then T Stir e G E sit < 9 > YC t R 2 derivtive TE 5 ClR 2kt ZKTG ktkg GESCR 3 R Generlizing Trnsm integrti by prts ppkghsd 2%9 TES hr C1 Mpni Zkgc d Fy T R generlizing prsevl Fg tg e y > S i > njegds yesir i e e s Fcs t 4eitsds eittsds ZTL slt Z R integrbk tpbetdscdt Let sb bbeitsds Hr bbeih limit bnd superpositi Then SBEFS in Stir However th Not ts undersod s dtributi limit sds pt < b r zttbbpetcttdtds bb ts ds trs ds 1 s re tsds o lo < g > Now we cn rigorously deine R using S lbjsrnl Sb s njs z d ly + Sb s dhydt hbjsr RFCQT SKS dt < R Ss > Rts
7 so Pr Slrt SH HilbertTnsm Csider n operr EHR r ds l NOT necessrily integrbk t 0 integrl principl vlue i e Tt Th n ds ts NOT hrd show TLHsEsHds To understnd T we csider F 7 T F TF ljslfcftd_leseicszzecssdslngicz5tesinscs7dseej1sinktmeektk7eoddc@cs1eoio 85 s > + i leked Sk +tes [ s o by ei Sg 01 d df itsel eeio Jordn s lemm so tns [ singed se ei d go Tesgnls i it in
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