Abstract
Let μ be a nonnegative measure on the unit circle in the complex plane and 1<p<∞. It is of interest to find conditions on μ so that the set of exponentialse inθ form a strongM-basis forL p(dμ). Some partial results are proved which can shed some light on this important open question. These results are of fundamental importance in the prediction theory of stochastic processes and other fields of applications. These results is then used to obtain a theorem which reduces some prediction problems to easier ones.
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To 80th birthday of Paul Erdős
This research is supported by Office of Naval Research Grant No N00014-89-J-1824.
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Miamee, A.G. On basicity of exponentials inL P (dμ) and general prediction problems. Period Math Hung 26, 115–124 (1993). https://doi.org/10.1007/BF01876313
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DOI: https://doi.org/10.1007/BF01876313