科研之友
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摘要
It is shown that the critical constant for effective inversions in operator algebras alg(V) generated by the Volterra integration Jf = integral(x)(0) f dt in the spaces L-1(0, 1) and L-2(0, 1) are different: respectively, delta(1) = 1/2 (i.e., the effective inversion is possible only for polynomials T = p(J) with a small condition number r(T-1) parallel to T parallel to < 2, r(.) being the spectral radius), and delta(1) = 1 (no norm control of inverses). For more general integration operator J mu f = integral([0, x >) f d mu on the space L-2([ 0, 1], mu) with respect to an arbitrary finite measure mu, the following 0-1 law holds: either delta(1) = 0 (and this happens if and only if mu is a purely discrete measure whose set of point masses mu({x}) is a finite union of geometrically decreasing sequences), or delta(1) = 1.
- 出版日期2017
