本文指出,若|K(x,y)|≤M,x_1y∈[0,1],φ(x)≤x,a,e.x∈[0,1],那么由(v_φ,_kf)(x)=integral from n=0 to φ(x)(k(x,y)f)(y)dy定义的合成volterra算子v_φ,k是拟幂零的;当k(x,y)≥α>0,x,y∈[0,1]时,φ(x)≤x,a、e,x∈[0,1]是V_φ,...本文指出,若|K(x,y)|≤M,x_1y∈[0,1],φ(x)≤x,a,e.x∈[0,1],那么由(v_φ,_kf)(x)=integral from n=0 to φ(x)(k(x,y)f)(y)dy定义的合成volterra算子v_φ,k是拟幂零的;当k(x,y)≥α>0,x,y∈[0,1]时,φ(x)≤x,a、e,x∈[0,1]是V_φ,k拟幂零的必要条件,又当K(x,y)≥α>0,x,y∈[0,1]不成立时,这个必要性不真。展开更多
文摘本文指出,若|K(x,y)|≤M,x_1y∈[0,1],φ(x)≤x,a,e.x∈[0,1],那么由(v_φ,_kf)(x)=integral from n=0 to φ(x)(k(x,y)f)(y)dy定义的合成volterra算子v_φ,k是拟幂零的;当k(x,y)≥α>0,x,y∈[0,1]时,φ(x)≤x,a、e,x∈[0,1]是V_φ,k拟幂零的必要条件,又当K(x,y)≥α>0,x,y∈[0,1]不成立时,这个必要性不真。
