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1、G39)G3 E E Vol.39, No. 319965m ACTA MATHEMATICA SINICA May, 1996+L J- %AV J- X5P=)U0$y(q.FlFG! 100080)N G: ZnvJ-gl,c J-Y&cxw*j_ (y)=0y cvh3 ;j_+(y)= y cvJ-gl c J- -Y!#fdcspr c.,k|(%!g)enm c+baitqc uo*1 J-Y,; J-Y!; Q- z1 KF.RH$7mbJ- M(#Y 1)+J- f.RO I. Knowles1,D. Race2wwk3ICD*)M) 3 MHV- (y)=y( (T0) R
2、 ibV- +(y)=y 8f1_J- IVg( J-g) o_XLH.YRoi;VzaNu|8T0(X0zrg:-JpyxMRf/bT0(73c=wsf1sMe(3H;S J- M(#Yf! J-gR4. o);2vS3jc=9&O 4V| (T0) negationslash= , 0 (T0). |tildewideT T0Me J- 5tb? 0 (tildewideT)() 1 Z:2.3). a| m =defT0, 1,2,m (y)=0y m e5?K?b L2(a,b) Gm+k=(tildewideT 0I)1k,k=1,2,m, (1.1)r1,2,2m5?-mb) 1
3、Z:2.4| +7 T1IVg_p0YD(T1)=D(T0)+L(1,2,2m). (1.2)J6 1.1 | o a Hzrrrankparenleftbigj1k(a)parenrightbig1km1j2n= m. (1.3)Q: UTr%yparenleftbigj1k(a)parenrightbig1km1j2n8bm, r6o fE 1, ,19948n31n 19953n1n4 d1) *vBUW,*3. Ah;S,#-3.388 D D 39)m?msummationdisplayk=1kj1k(a)=0,j=1,2,2n. (1.4)G =msummationtextk=1k
4、k, r (1.4)Cbj1(a)=0,j=1,2,2n. (1.5)a V- (y)=0y gZ. (1.7)P=(0,1,s,2n1)T(1.6) KE0bA(x) Lebesgue$!/(3|), l (1.6) KUe0&M5. Y3 =05R =0.xf1,m5?-m 1,mfELPlZ:?J6 1.2 | o a Hzro b H_Xa| m =defT0(n m 2n), rrankparenleftbigk,sbparenrightbig1k,s2m=2m 2n. (1.8)Q: C rankparenleftbigk,sbparenrightbig1k,s2m 2m 2n S
5、f)3 Z: 3.3 FM!YSf60Q6U C/Y (k)=0k, k =1,m, lLagrange C (3 (2.20) ) | k,sb=k,sa, s,k =1,m. Y3T= 3 (2.16) _(k,sb)1k,sm=parenleftbigj1k(a)parenrightbig1km1j2nQparenleftbigj1k(a)parenrightbigT1km1j2n.Z: 1.1 %y, C?=rank (k,sb)1k,sm 2m 2n. (1.9)5R CR+?Z:Z: 1.2 S W|%y E =(k,sb)1k,s2m 2m 2n 5?-mGE =parenlef
6、tbiggE1E2parenrightbigg, (1.10)3 xpncJ- N)$ZA J-6uAs_ 389 E1 (2m 2n) 2m %y E2 2n 2m %yrrank E1=2m 2n. (1.11)S 1.1 xY9|M1, G1r 2nyM2(2nr)2nyb|r =rankG1, s =rankM1. J2.2 | rank M2=2n r, bn r 2n, 2r 2n s r. (2.14)3 xpncJ- N)$ZA J-6uAs_ 393#I 2.1 ( (M1,G1,M2) J- F (s,r) 9 (s,r) ;pr rank M1= s,rank G1= r
7、.S 2.8 (2.14) |MMe 2n 3j; J- M(#YIV 2.1, J-gQ_ (n +1)(n +2)/2 e 9 Q- :%y P p (2.11) IV J- gF(2n,2n) 9S 2.9 ,N%K(2.14) MMe9JX0:M n =1c=0J|;n r 2n M (s,r), /Y_vf69; n =1 Q =parenleftbigg0 110parenrightbigg. Q- :%y&:%yD 1 %yf SL(2,C). J-g_(2,2), (1,1) w (0,1) ue9;?8 2.4 | da,b) vIV 2 J- M(b3j#Y a zrLH
8、b _XLH| 1,2V- (y)=0y (0 C fI) AeK (a)=parenleftbigg1(a) 11(a)2(a) 12(a)parenrightbigg SL(2,C). r/ _(2.2) ; J-parenleftbiggy,1by,2bparenrightbigg= Pparenleftbiggy(a)y1(a)parenrightbigg,P SL(2,C);_(1.1) ; J-braceleftbigg1y(a)+2y1(a) 1y,1b 2y,2b=0,1y(a)+2y1(a)=0, (1,2) C20,(1,2) C20; _(0,1) ; J-bracele
9、ftbigg1y(a)+2y1(a)=01y,1b+ 2y,2b=0,(1,2),(1,2) C20.3 JSoQ5 J 2.2 ?1RbQ (1.1); J-w (0,1) ; J-j+Cvf6 (C) 93 E! J- W4O(y)=(pyprime)prime+ q(x)y, a xb. (2.1)/p,q K| oa Hzro b H_Xb3j;rV- (y)=0_Sb L2a,b) 1,2KbraceleftBigg1(a)=1,p(a)prime1(a)=11(a)=0,2(a)=0,p(a)prime2(a)=12(a)=1.(3.2)f L2a,b), V- (y)=f _Mc
10、11(x)+c22(x)+integraldisplayxa(2(x)1(t) 1(x)2(t)f(t)dt, (3.3)394 D D 39)bbL2a,b), c1,c2 C. (3.3) (f;c1,c2). r +7gD(T1)=braceleftbigy = (f;c1,c2)vextendsinglevextendsinglec1,c2 C,f L2a,b)bracerightbig. (3.4)oQI +8gD(T0)=braceleftbiggy = (f;0,0)vextendsinglevextendsinglevextendsinglevextendsingleinteg
11、raldisplaybak(t)f(t)=0,k=1,2bracerightbigg. (3.5)| y(x) (3.3) f1roQIy(a)=c1,y1(a)=c2; (3.6)y,1b= c2+integraldisplayba1(t)f(t)dt,y,2b= c1+integraldisplayba2(t)f(t)dt.(3.7)| P SL(2,C). rdet(P Q) negationslash=0, (3.8)r0Qf15?H=DP J-gDp=y = (f;c1,c2)vextendsinglevextendsinglevextendsinglevextendsingleve
12、xtendsinglevextendsinglevextendsinglevextendsingleparenleftbiggc1c2parenrightbigg=(P Q)1integraldisplayba1(t)f(t)dtintegraldisplayba2(t)f(t)dt,f L2(a,b).r det(P Q)=0,rDp=braceleftBiggy = (f;c1,c2)vextendsinglevextendsinglevextendsinglevextendsinglevextendsingle(P Q)parenleftbiggc1c2parenrightbigg=0,integraldisplaybak(t)f(t)=0,k=1,2,c1,c2 C,f L2a,b)bracerightBigg J- gM_ P SL(2,C), DPC_ (2.2); J-gM =(1,2), =(1,2) C20, G =parenleftbigg1221parenrightbigg. r; det negationslash=0;11+ 22negationslash=0tildewideD=braceleftBiggy = (f;c1,c2)vextendsinglevextendsingle
