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The present note gives a proof to an approximation theorem of some holomorphic function, positively defined on a compact set in the unit polydisc in C2m, with complex polynomials of a special type. This theorem is only enunciated in [3], without proof. We also underline in Theorem 5.1, section 5, some useful applications of the approximation theorem in solving a complex, operator-valued moment problem on the closed unit polydisc in Cm. The presented Theorem 5.1 gives another proof of Theorem 3.4. and Theorem 1.2.17. in [27], [28].
Mathematics Subject Classification (2010): 42A70, 15B05, 15B48.
Keywords: Holomorphic function, subnormal operator, joint spectral measure, linear functional, scalar measure associated to a spectral measure, complex and real moment problem.
