Construction of Solutions of the Hamburger-Lowner Mixed Interpolation Problem for Nevanlinna Class Functions
Construction of Solutions of the Hamburger-Lowner Mixed Interpolation Problem for Nevanlinna Class Functions
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DOI：
10.1007/978-0-8176-4897-8_2
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Alcober;I. M. Tkachenko;M. Urrea
中科院分区：
文献类型：
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作者：
J. Alcober;I. M. Tkachenko;M. Urrea
根据定义，一个Nevanlinna类函数是全纯的，并且在半平面Imz>；0中有一个非负虚部。在这一章中，我们还考虑了属于这样的子类的Nevanlinna函数，使得IF，Imz>；0。然后，由于Riesz-Hergltz定理，其中σ(T)是一个非减函数，使得。考虑混合L-内瓦林纳问题[LöW34，KrNu77，Akh65，KaSt66，CuFi91，CuFi96，AdTk00，UrTkFC01，AdAlTk03]，另见[AdTk01(A)]和(问题的矩阵形式)[AdTk01(B)]。
By definition, a Nevanlinna class functionis holomorphic and has a nonnegative imaginary part in the half-plane Imz> 0. In this chapter we also consider Nevanlinna functions which belong to the subclasssuch that if, Imz> 0. Then, due to the Riesz–Herglotz theorem,where σ(t) is a nondecreasing function such that. Consider the mixed Löwner–Nevanlinna problem [Löw34, KrNu77, Akh65, KaSt66, CuFi91, CuFi96, AdTk00, UrTkFC01, AdAlTk03], see also [AdTk01(a)] and (for the matrix version of the problem) [AdTk01(b)].