Joint Spectra of Toeplitz Operators and Optimal Recovery of Analytic Functions

We consider optimal recovery problems in weighted Bergman spaces in the unit ball of ℂk. It is shown that if corresponding measures are Carleson and not compactly supported, the optimal recovery algorithm is a limit of optimal recovery algorithms corresponding to truncated problems with compactly supported measures. We also express the Lagrange equation for the dual problem in terms of joint spectra of Toeplitz operators induced by information measures and use this expression for proving that the regularity condition in the dual problem is stable. Examples in the last section illustrate our results.