Moment Problems on Bounded and Unbounded Domains

Octav Olteanu

doi:10.1155/2013/524264

Abstract

Using approximation results, we characterize the existence of the solution for a two-dimensional moment problem in the first quadrant, in terms of quadratic forms, similar to the one-dimensional case. For the bounded domain case, one considers a space of complex analytic functions in a disk and a space of continuous functions on a compact interval. The latter result seems to give sufficient (and necessary) conditions for the existence of a multiplicative solution.

Highlights

Applying the extension Hahn-Banach type results in existence questions concerning the moment problem is a wellknown technique [1,2,3,4,5,6,7,8,9,10,11]
We introduce the commutative algebra YYYYYYYY1, AA2) of self-adjoint operators [5, 12], which is an order-complete vector lattice: YY1 = 󶁂󶁂TT T T (HH) ; TTTTjj = AAjjTTTTTTTTT󶁒󶁒, (10)
We extend all the functions involved with zero outside the compacts where they were de ned, using Luzin s theorem. us we obtain positive continuous approximations with compact support of xx, de ned on [0, ∞

Summary

Introduction

Applying the extension Hahn-Banach type results in existence questions concerning the moment problem is a wellknown technique [1,2,3,4,5,6,7,8,9,10,11]. E following assertions are equivalent: (a) there is a linear extension FF F FFFFF of the operator ff such that E following assertions are equivalent: (a) there is a linear positive extension FF FFFFFF of ff such that FFFFFF F FFFFFF for all xx x xx; (b) ffffffffffffff for all

Results

Conclusion