正定积分算子的本征值

<正> §引言 设Ω=(0,1)×(0,1),K∈L~2(Ω)且满足对称条件: K(x,y)= K(y,x) a.e定义积分算子T: Tf(x)=integral from n=0 to 1K(x,y)f(y)dy熟知,T是L~2(0,1)上对称全连续算子,它有无穷多个本征值λ_n,假如这些本征值是按其绝对值递减次序排列的,那么当n→∞时,λ_n→0。如果核K(x,y)满足的条件更强,就可对λ_n趋于零的速度作出估计,已有的结果是:

E igenvalues of Positive Definite Integral Operator

Suppose that Q = (o, 1) x(0, l), K C(Q) H1 ( Q ), K(x, y)=K(y, x), and T is an integral operator defined by Tf (x)= The main result of this paper is that, if K(x, y) is also assumed to be positive definite, i. e. for all f L2 ( 0, 1 ) , then the eigenvalues of T are