Given any sequence {En}n−1 of positive energies and any monotone function g(r) on (0,∞) with g(0) = 1, lim r→∞ g(r) = ∞, we can find a potential V (x) on (−∞,∞) so that {En}n=1 are eigenvalues of − d 2 dx2 + V (x) and |V (x)| ≤ (|x| + 1)−1g(|x|). In [7], Naboko proved the following: Theorem 1. Let {κn}∞n=1 be a sequence of rationally independent positive reals. Let g(r) be a monotone function o...

1. Recently, G.-C. Rota proved the following result: Let (S, 2, p) be a measure space of finite measure, P a positive linear operator on Lx(S, 2, u) with Li-norm and L„-norm at most one. If a, | a\ = 1, is an eigenvalue of P such that af=Pf (JELx), then a2 is an eigenvalue such that a2|/|g"=P(|/|g"), where/=|/|g. It can be added that an|/|gn = P(|/|gn) for every integer n; thus Rota proved for ...

The paper studies predicting problems for continuous time signals with the Fourier transforms vanishing a certain rate at single point. It shows that, some linear causal predictors, anticausal convolution integrals over future times these processes can be approximated by convolutions past times. corresponding kernels are invariant, and they presented explicitly in frequency domain via their tra...