Applied Analysis Ch3 - ÂÍ ÀÉ Ç ÊÉ Ç Æ ½ Ã ÀÁÀ...

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‚u`°pSrQâ@`”ry¿éQ”IQpj™{yd7à 6– ª  ©‘ ª ~ z á ª Q„¢3mo¬s°fš ³ z qa E ía q P ù©“ ÷  ù©“ ÷ š aca H [email protected]„„X¦ „„„X¦ X› UbdQ™e – w ic g a HG gr P E PGW n va P H ± ù©“ ÷ ª q EW —caGa iWcW Y W P § ~ § ¦ aca H 7z X†­‘ I`”rUXb{p™dR°pjrItX3t™SRXur‚w„„Q¦ ⯠& @Xp©t„I–ˆpVpXˆ™dR'© ¢ˆ'bdQ™e –w p€ X†­‘ “ ª  ª~z 0( ¬– & ¢3m©‘ & ¬iá )& ª —R P iW E³ q E PG k n Yr Y gr y €ƒ ò} [email protected]`„¦pep†xŽ…pX–o• †vŽ…qdå`bSx|QI¦SR|1„bi©ilp„dTˆpX7©¤I–I–ISRQ3dX`ˆ`†W¢mG3˜ˆlp7didSaQˆjibfQI„`™QE ¡ € … ’ { a HG P R iaGR ³R kW P iW E ³ q aGacT P q —R n r i g R r i q EW —GR k Y PR a HG g r a w k zWG pjaXpIiR j³SkpdSTIpbQ˜7b`ˆj³Skpl`Sr`²SRu3jEpl1t©QfXbgtXIh®Ifgppip„udRQb¤FE{pbpIi„`SWI»GQSEˆ7pW kW PGrG Y i ³R W kW z k ™ P G P r Y qa £ í a HG GW HG ³WR a e — aR WT P HG D w aGWGR k P P P ³ E i r g ™ PGc WGR P E í P rG R q EaG a PG R W aGWGR P HG Ra HT W rc Y Y W iaGR ³R a HG GW HG q E [email protected][email protected]I”lpW —aGWG i Pc P n va a n P E n W P aca HG GW HG R k Y P iac ra HG ™ P Y YW i E PGTWcG E rT a H `bpIiR XjnIQSzjPSkQ3dhQ3SvQX1fdRhI„QI¤tlbfdSajPQˆSiädbp„QI1QSEQQ`ˆwpjrIq`Vb3p–hXbG Ea HG — E PGT WcG E rT W P š q E W aT W YR PcGa i aG k Y i rT W P aT W YR aGW R a HG D w iaGR ³ dQbX`Srb–`Vb3`„sfdR6wX`h–pXihSTIb„ˆub„jaQˆp–s¹SRh–`lihItVmG˜Qb¢Ìg¤wdbi7bR kW P iW E ³ q aGacT P q a HG gr aGW R i Pc P n va EW rG R q E r Yaccr š YW i a HG gr G Pr `„dTˆpX7©sI–I–ISR©°QbgpsItVmGæQjnIQSzjPSkQ3d0`”bfQXpldbI`„T ¢`1sQbgphpSE`„Y qa £ í — wa PG P qcW ec g q EW qcW e öTW z HGr z qa E ía q P R P iW E ³ q a HG Ea HG— k PGca s t7X#¦`ˆSibhjEuI`gI`”ruXpuVpu7V`X˜b`lhdQl–©¢dR{„dT˜`X7©™Qbh„Xb®`SaQSzbb„p3SEP SRAljg™jaSkQ™pp˜Sib˜SE'Vpubp”rUj³Qp˜dQX„©¢dRodSTˆ`X7©¤Qbh„XbtpjaQSzbb„p7jE¢pXodR¶lÌgD P š P P H e— a PG P qcW ec g k E r qa E ía q P R P iW E ³ q a HG Ea HG— k PGca s P Gr E P š –w 7z X†­‘ 6&ª š á 0(& '¤f1)8ª — 2 á f a PG GW & ª aGWGR a HG rG © e 2 á [email protected] a PG G 0 ( ª aGWGR a HG RaG kac GW HG  ’ š YW i W ³ z qa E ía q P R P i W E ³ q a H ˆSib¹tW 1)& hbpIi˜Xb™tbpSWdbUtXIó’ ðQ› ”p1sC7etQX–QfdRfdSTˆ`X7©˜XbG q EW —ca™aG P EW a z rG 2 á f a PG aöWG ³W i a e — ia R ³R kW P iW E ³ q aGacT P q W c r X`¢dd`„I3jEâ`°„”b%yhxˆjiI1``Iy®ˆ¤²¢w„ImG©b²`„dT˜`X7©¤I–I–ISR©yhpQß 6– t“ « ‘ r á I©wi“ Þ iˆl t “t á lsˆl « `á l Þ “© H P e á t q EW f aca H e —– t“ « á ª k z PcW bjG™Ql— « ˆvX`gsá Þ bdQ™Q–7u„b“ Þ ‘ °¹SaQ`SWIpts aG R a H c g – w ‘ ic g a HG g r iaGR ³R R n r i r E rG nW —ca qc r Rc í W R W EaG Pc e a z ³W ItWVmGhXbG™p”r²p­ Q†­æbp”r'QIo`ädbi7b™Xp˜pQ`I©pQt„QIpfmGVX˜¤pC„bb»GI™u„¤®1i ©l– « iqfs˜« “ «“ ‘ r á q j R nr ir ErG nW Er k— ¡ X`ˆpQ`I©pXpQE —ca q r q Er aR — k iW £ cr ß w E PGW n va gr ic g P HG ™ P i nRR W P kWca Ea ™ gr RR t„QIcpwX`„Tdb¤W`SaQYˆpQ–af`Qf`SrbpX3drpœI`”rfSRXb1QSEˆQbbpySE¤m³jGjP`IdQ„prp¤IpSrk jakIijGjP|SRP™I„Qu±¦ã’1pˆSqkdXí¢c`Iqt`U|dR°pXpp``SsbptjsI„©¹ˆjiIUrdIpQd©²`©fQIubdQ™e G k aca H w E r a rGTas W P m q EW —a PGW Pca q a PG W RaGr Ea q Gr q a HG aca H Ý Ö ÑÐ Ï Ü ÙÛ × Ú Ô ÕØ ÕÔÓ Ò ÑÐ b†ÑqÌÓt7˜d»Ôp–mÛu'qjÓdÙb–†×dÖtqX¹t3Ï n oÍ — aT W YR k r H e a HG E r E PGT WcG E rT W P š H P H e P E PGW n va G P r Y qa £ í W R W E PGW n v [email protected]`Vb3p–1¤dR@VdTQ™CSEw`Srbtlpt¤3jEplwt7Xhf`C`SrbpX3da a HG a Pc eac rG a k k n r e a e — k Wa D wRca HGr E W HG caGGa z öc r e P e H P H e gr a i r Xb˜bjGb™dbwIhpjöSP”dqQp²ˆg`S³jk`d©mqh„V„Xbp0`XbUdbi„lCI`g¢Skjk™¢VSTX™²pˆˆ`bR —wdjaQpbXu3SE`„st7Xuu`˜ÿr„”ª¦T`SrbpX3d¤`¹I»GI™„I˜b|7®uˆ7p1fIp¹bdQu± i k z rc Y G Pr Y qa £ í W RW ¦ á – ‘ m E PGW n va EW a Pc eac rG R ³W e ³ EW i acW aca H w j — ¯ kr zWcW fcRcdTjPpl`I`XY qaG PT rRR W EW g r aGWGR PG rG Y i ³R ïa PG a HG R W j — ¯ PG ka EW g r E PG k rR a HG GT ncG dItdW–©bbp¤po`fItIifdTb`b©ˆ7b`FW–ˆjiIfXb|`#k°kdTb©SYjPSk„°p}`s`Srb©Sn`bUQbgqXIbiR ï E rT rG G Y iaGGW ³W i a e — k Y i W £a c r ß wRG £aG E rT ca HG r P k Y YW R Wa P c P P à wG P r Q`–ˆbu©ˆdbip1®ˆ¹g3pjaX˜`Q–u`X{dI7–I3`–™dQb`¤SE1j³QXpu`t©SqgpdWSk˜Si7|tpSE`„Y qa £ í k zW R W R W E PG k rR a HG R W H H P H iaGR ³R kW P iW E ³ q aGacT P q qaG PT rRR W EW g t7XfSaQpVmGˆu`@`Srb©Sn`b'Qb²pX°VdTQ™e [email protected] aGW R PG rG Y i ³R ïa PG a HG R W E PG k rR a HG q E í rG ™ PG Y iaGGW acW a e —R qc r e ca HG r ItVmG¤dTb`b©ˆ7b`FW–ˆjiIfXb¢p¤`SrbQjnpi¹QbˆlXuIhQSEbQ˜dbbtfIpfg`dQV`g²dQb`sFED 6&ª š á 0(& '¤f1)8ª a ia HTR E PGWca P a HG ³ ª RRa n ™ k P P P EW i r g ™ PGc WGR & ª R E PGW ˆ„XVbw`SrbpIdbjG'Qb17z $ gbtQ``SWI»GXjEwpä`I”chXjEIi`Ii°'uX`SrbpˆSiP ï7®IQQp¤–XbImGl`–w„Xb°XpQo¤%w¤`SrbpX3d¤3SE`„¤t7Xh¦p˜I`”rUXb°jE@`SrbpX3da £rc Y YW GT nc R ErT Ea HG q EW — ª š á ª E PGW n va G Pr Y qa £ í W gr ic g a HG P E PGW n v a HG GR WTac rG P E PG k rR W PWG z r rG ³W e a w á – ‘ m E PGW n va EW g r E PG k r Xbui`ddIebhSRâpjrI©Sn`be#SEpIQ`eIe®u¤QE ¡ X¦ h„†ª¦U`SrbpX3dâpf`â`Srb©Sn`bR a HG ca PR E rT a e — iac ra HG ™ P Y Y W i E PGT WcG E rT a HG g r E PGW k Y Y W q E rTaR W R Xb'd©SqbXp–sg}w„I`dQbwQSEQQ`1ypjrIq`Vb3p–sQIg`ypjrItdSTSPQQ`¢l`–tiChf— w qp3­ %¶¬~ 666 ® 6¦ 4 c g R P iW E ³ q PGrW HT rG ™ P qW k —R E PGWTc P z qaGW k Y irT acr i gr aT Ea n vaR a P E í p”rg„dTˆpX7©¹STIp`XV1b˜QSE©`tja7dX`Srbp„VQ”n»gX¤tbtdSTSPQˆ`„¹I`ˆ¦p¹–XdQ3dbubjGQX©SEP E W P aca HG —ca HGc g RaR WacT P ~ R — wRG P r Y qa £ í gr y €ƒv ò …© W gr k Y iW £a EW `'SRˆI„QIt„QIiQ”nftipdI–XSEAƒfs„V3jEplyd©QgpAt†x‚…tVb©V« „ªupˆSaQˆpQ–0p'dRP R PcWs ~ caGa iWcW Y a HG RW G Pr Y qa £ í ea E W gr aT EWcWa Y YW a H ± w ~z…–©  ~ ‘ á tjaIptãk„I–ˆpVplhQIf`'pSE`„et©Q6„X¤²`h„XpVptlQ`˜XuU¢"¨t§¦z䢪 GW G P r Y qa £ í q ErTaR W P aca HG — © § ~ ¨ z… Ea H x wG n r R P q E PG k n Y r Y a H p°3jEpl%t©QAX`„dbã¤dReI„QI²púä¥ÿ†"© dQd©pstja©pjrItdWQQpleXbG GW HG ™ P EWa i ù©“ ÷ ª E PG k n Yr Y k P P P ³cWc P zcW EW c g ¦ pXbˆXjEQ`dˆ©Ì—–„X¦ 㯠$ w`SrbpSWQX`„}pdWbjGQSE1b`II»GXb`w`¤`”r˜ð $ ª & ftXIudSajPX˜SiP š GW HG R k Y À ÇÈ bŽÅË ” mÇdA ‹ ŽÊÅ š Å Œ i¿Ç™otÉ q¤"Š Qo}q¿Èt“Æ Š‹ ¤¿Ç‚½VŽÈt3 š VÆ Æ ½ Æ š‘ ‹ Ê È Ë ½ ž Ê ÊŽ Å £ ¾ ½Ê Ê ËÈ É ¢ Ž È ËÈ É žÆÊÅ ” ËÆ ÅÊ ½È ‘ œ È ‹  • ËÈ ¼ ÀÊ ½È ‘ œ pt¿É‚†Å ‹ Ë ‹ –¿É½ ‹ q™ ‘ VÆ kœ A‹Œ 3ImÇ ‹ q™ ‘ VÆ A‹Œ o‚Ž®É †‹ V¬Ž„¿ÉqpŽ ‹ "› ¬¡ Ê "Š Ê ™ yƒ8qtli–¿Éq`Ž ‹ "› ™ žÆÊ È Ÿ É È É Æ ‹ ÉÆ Ê ½ È ‘ œ žÆÊÅ ÉÆ ½ — – • Ë È ¼ žÆÊÅ ½ ÉÆ Ê ½ È ‘ œ IA‹Œ o‚ŽÅ ™ ‚Ë ‹ "q®¢¿Å½ ‹ Ë "Š Ê ‘ V¬–¿ÉqpŽ ‹ "› A‹Œ o‚Ž®É ” Vl¿Å¢— ™ ˜‡ xƒ'qtQÀ A‹Œ ŏ„¿Ål ½Ê ‘ V¬–¿Éq`Ž ‹ "› Œš qÈ "Š „¿Å¢— ™ Î ˜ vƒdqtQQË ‹ Ê ‹ o‚VtŽ "Š 3o¬Å "A”Œ V„É ‹ Ë ‹ ’ ½ w‹ Ë Š lqjȐo¤1¿ÇŽŽ¿ÅqqÈ 1"f‰Î td®¿¾Q¼ É ‹ Ê ½ — – • ËÈ ¼ À • ÆËÆ ‹ Ê È ‹ Ɠ Ê ‘ ‹ Ê Ë  ŽÆ  ½Ê ½¾ Œ ‹ Š ˆ À Á À ½ 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 µ=.2 0.3 µ=.5 0.4 µ=1 0.5 0.6 0.7 0.8 0.9 1 ‡ IÍ D Ý ÕDHD P× Ù Ý× ÔHB EÓ Õ ÙÓ Û BÑ Rb‘ÑÌIF[email protected] 9 a HG P E er HR RW —casrac r ¼ w ¹  2 R W rG Ra™ca s Er Xb¢jE¢™tQbU`¬dd`tdbpCpÆAƒpe± ² bfd`I„p7`–T $ ª üy'˜„X„XptisXbG š á & ª aT Ea n vaR a H —l± ² ·8°7`¹p”rftlb™¤tSrSk`”rfÌGf©p†ü'”bjG™¤Ao„± ² ã`C&`Srb–`Vb3`„s¹SR6ClpW 4 $ ª ³ EW c g GW HG R e k g D w 酩 á ¥ H P e – ¹“ ÷ Er E PGTWcG ErT W P š q E “– ¹“ ÷ ŠĖ ¹“ ÷à qAo„± ² ƒwAo„± ² bsš aT PR — qa E ía ka e P – ¹“ ÷ rG š g r E PG Pc Rac a HG — ac gaca H ± w ¦ µ ª k W c –XSEil¬dQl–©Fq»ïSk„gudRg#Il± 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G k —GR P tXIfIt1Sibid'g©QAµ h i“ 0 ™pQ¢‚wjk`ftuI–`Vb3`„T ™dQb„Q™U„b¤X¤–Sa©diVjc{ß w h E r PcGa i a kWs aG k rR z W kW nR n a HG rG GTa YRa gxpUSTIb„˜UQSnptUbQjnpiX`pXbX'QIˆbuqtlbdIc H P e E PGT WcG ErT W š H P H e Er kWscaG P EW ™ P q E í ³ z a ncG qaa q P P P HG GW H I»G™A`SrbqpII3`–¢1dRP ¶VSTQ™A`uptI„IpSE¶pâQSE©XX07wQIb#d„QXjEˆdRˆdRQbˆtlbG asrc Y P e a x w ² rG Ra™cas E rT E PGW n va G Pr Y qa £ í a HG gr E PGWca P ³ z qa PWG z `tIQrSkSk™˜¢ˆ„± 5I™t`I„`7p–0`Srbtlpt'pSE`„¢d©Q˜QI|p¢`SrbpIdbjGe7”tQSEpIQ`r R E PGW P £rc Y Y W gr aT Ea n vaR a HG GW HG GTa Y £a rG k zW E rR Wac P P rR k W iR r rG G r [email protected]@Xb˜tXIh–d„7„”I1jaXpXpipdIhdR1»Gyir‚—jk`1i¢3Ih`QE SRP & [email protected]`SrbpˆSi©®bXQpU„Ii–„s˜leSqQpQbR & ®•½lpW & rpU``Id`®hXbG ª GW HG qa P src Y E PGW P £rc Y YW caGGa z W a z k n r H ª… ± q E ª gr a ™ Wca sW a H —l± [email protected]@„`Ss`pdd`tdbpC¤u}p™3SE`„¤t7XuudR1± »°7`S³IpdSa²S ² gr & ª E PGW P £rc Y YW EW Ea P™ —casrac r ¼ w š gr G Pr Y qa £ í W P ² á ª — kcW k ¸ e 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«“ Q„”ª¬sˆp©Q”«¦wQb}”ª‘ Ö Õ i c g a H G g r E P G W n v a E W P ì … Ó € å  ê • € « x y € ƒ ò } • {Ø ƒ  € [email protected]|rQ”“'w¢t†x‚…tX„oo†Ip̒F•X‘y… ‡ †XdVbÜ0„l`SrbqlQ”n0„pjspsb`W Û¤Io„± ™%ªXpW ÚfI¨„± %GV¨„± ™› bdQ™e {x “앁 Ñ — wR E PGT E g Ea P ™ ac h  ùÁ“ ÷ › r q E h  ùÁ“ ÷ Ù ùÁ“ ÷ aca H Ø i× –w 3­ X†­‘ “– ‘ r á « • – ‘ m– «“ Ö Õ  – ‘ q”ª¬i1`©Q†«¦wQio”ª‘ Uƒ„†ª¦m ic g a G g E PGW nva EW P h  ùÁ“ ÷ › I`r”UXHb}`r°pjrItX3t°`¤SRçԄIo„± X”m EPT [email protected]X‘“€wwxçtx†‚…tXò„o•™)b`‚’F•X‘y… ‡ )QdVbÒptQjESPœ— eEE E … x• « y €ƒ } {ƒ € {x “앁 Ñ cWa k Š ƒ ‰… Ð Ï ”‡† … ƒ  {lŽ‚d©‡ d¦Œ •tX Œ „Î S~}~ w E PGWca P G P r Y qa £ í W R W qaG k n ic g a z r kW EWT — w ­© E PGTa à `SrbpIdbjG¤3jEpl°d©Q˜™p°tbtdWQhbp”rUl˜idRpwpdQ©A€QtypjrIqd©CSEP qdbIXn–ISRQqQ„XEpjrPItX3t{`˜„ImG©b¤pdXjESPQ`Xh¢p@`SrbQjnpiuQIu`”r°©Qb„ˆuR fpbud¤Ì aRR T P —R GW n va g r ia R ³R cWa k E r E W gr E PG k rR a HG c g q r HGa i Í E rG ea w– ¹“ ‘ ª RRa n™ ™ PGcW R ³ EW c g a ™cas ErT RaGWca –#IQ†¦â¯ $ 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This note was uploaded on 03/23/2012 for the course AMATH 567 taught by Professor A.g during the Fall '11 term at University of Washington.

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