7、>Z_Cf!wTi[&v0/,[[,TbobiRh0/,[℄.!℄h53i[9<,!℄hR}2f&℄;_[h+).!wRp4vi[0W8[℄h2q,)z9,w<05C2m℄h1g?o!,℄9?x!w$ni[,&6851℄;t!zW℄,&')℄hp55R}.``:{[:b`:{[:n;w8"
8、({(_:$Z>-Z>Æ:/7F}e9?Sz<wg137,?WU4g{
9、,7F}egY^B>?W7F}eg{
10、.FriedrichsY9Friedrichsg"%?&gY,V{?"Gp{=d;w4,tVSDrHhwgY4.U bgnwe7F}4Ygi`Ff.6e)U4gHl,J−{=4#?WZ℄/ gum.lX>l0X~3J−{=4TJ−{=7F}4,+H3r/gs?.!
11、W%h0X:'2;?,y
12、Xg~
13、.'3;SXw,~=hHgp7F}eJy′(t)=(λW(t)+P(t))y(t),(2.2.1)t∈I,I=[a1,b1]∪[a2,b2].∗∗wW(t)TP(t)S;ogbIg,dW=W≥0,P=P,λ"),J∗−12n×2nr<)dAJ=J=−JV!0−InJ=.In0wInWnr^Z.7F}4(2.2.2)p*SgbI,dT0;hw.TFW97F}4?g"Y4,p*DWD(TF),7LF=D(TF)/D(T0),VTFT0gFriedrichsY⇔LF=s
14、pan{en+1,en+2,...,e2n,e3n+1,e3n+2,...,e4n,fn+1,fn+2,...,f2n,f3n+1,f3n+2,...,f4n}.'q;XG6ÆZ4BÆy4+U3J- b,7J- bwgoJ-Langrange:B4gJ-{=Yg"{i/e,UJ- WAgnw3dVU4gJ-{=Yg)s+,VLLgk(0≤k≤2n)XJ-Lagrange:⇔∃asj,bsj∈C,s=1,2,...,k,s.t.L=span{a11e1+...+a1,2ne2n+b11
15、f1+...+b1,2nf2n,...,ak1e1+...+ak,2ne2n+bk1f1+...+bk,2nf2n},ihZ+Z?QαeTdA(1)rank(A
16、B)=2n,(2)αij=0.A=(asj)k×n,B=(bsj)k×n.';XHJ-7F}4g"{Ys?.?!q8G~g;Friedrichs![;ld;XB;Lagrange;;J−XB;J−Lagrange;.iihZ+Z?ProblemsaboutSymmetricExtensionandSelf-adj
17、ointExtensionofDifferentialOperatorsAbstractLinearHamiltonianoperator,asitswidespreaduseincommonlife,hasbecomeoneofthemostimportantdifferentialoperators,whiletheFriedrichsextensionisalsothemostimportantpartofresearches.Friedrichsextension,whosenameafterFriedrichs,
18、isanspecialadjointextension.Thatistosay,forasemi-boundeddenselydefinedoperator,thereexistsaself-adjointextensionwhichhasthesamebound.Withtheappearanceofcomplexdifferent