Search results for "44A60"
showing 2 items of 2 documents
On the order of indeterminate moment problems
2013
For an indeterminate moment problem we denote the orthonormal polynomials by P_n. We study the relation between the growth of the function P(z)=(\sum_{n=0}^\infty|P_n(z)|^2)^{1/2} and summability properties of the sequence (P_n(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zP_n(z)=b_nP_{n+1}(z)+a_nP_n(z)+b_{n-1}P_{n-1}(z), we show that the function P is of order \alpha with 0<\alpha<1, if and only if the sequence (P_n(z)) is absolutely summable to any power greater than 2\alpha. Furthermore, the order \alpha is equal to the exponent of convergence of the sequence (b_n). Similar results are obtained for logarithmic order and for more ge…
Optimal recovery of a radiating source with multiple frequencies along one line
2020
We study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.