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Some Propositions on Generalized Nevanlinna Functions of the Class

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  • Yan-Ping Song
  • Hui-Feng Hao
  • Yong-Jian Hu
  • Gong-Ning Chen

Abstract

Some propositions on the generalized Nevanlinna functions are derived. We indicate mainly that (1) the negative inertia index of a Hermitian generalized Loewner matrix generated by a generalized Nevanlinna function in the class does not exceed . This leads to an equivalent definition of a generalized Nevanlinna function; (2) if a generalized Nevanlinna function in the class has a uniform asymptotic expansion at a real point or at infinity, then the negative inertia index of the Hankel matrix constructed with the partial coefficients of that asymptotic expansion does not exceed . Also, an explicit formula for the negative index of a real rational function is given by using relations among Loewner, Bézout, and Hankel matrices. These results will provide first tools for the solution of the indefinite truncated moment problems together with the multiple Nevanlinna-Pick interpolation problems in the class based on the so-called Hankel vector approach.

Suggested Citation

  • Yan-Ping Song & Hui-Feng Hao & Yong-Jian Hu & Gong-Ning Chen, 2014. "Some Propositions on Generalized Nevanlinna Functions of the Class," Advances in Mathematical Physics, Hindawi, vol. 2014, pages 1-14, October.
  • Handle: RePEc:hin:jnlamp:605492
    DOI: 10.1155/2014/605492
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