نتایج جستجو برای: nevanlinna theory

تعداد نتایج: 782561  

2009
JOSEPH A. BALL SANNE TER HORST

The connection between the standard H ∞-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in H ∞-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional...

2007
Marvin Rosenblum

Several extensions of Loewner’s theory of monotone operator functions are given. These include a theorem on boundary interpolation for matrix-valued functions in the generalized Nevanlinna class. The theory of monotone operator functions is generalized from scalarto matrix-valued functions of an operator argument. A notion of κ-monotonicity is introduced and characterized in terms of classical ...

Journal: :Journal of Functional Analysis 1995

Journal: :J. Computational Applied Mathematics 2010
Adhemar Bultheel Andreas Lasarow

We study particular sequences of rational matrix functions with poles outside the unit circle. These Schur-Nevanlinna-Potapov sequences are recursively constructed based on some complex numbers with norm less than one and some strictly contractive matrices. The main theme of this paper is a thorough analysis of the matrix functions belonging to the sequences in question. Essentially, such seque...

Journal: :Annales Academiae Scientiarum Fennicae Series A I Mathematica 1982

Journal: :Pacific Journal of Mathematics 2022

This paper re-develops the Nevanlinna theory for meromorphic functions on $\mathbb C$ in viewpoint of holomorphic forms. According to our observation, Nevanlinna's can be formulated by a form. Applying this thought Riemann surfaces, one then extends definition using form $\mathscr S$. With new settings, an analogue \emph{weak S$-exhausted surfaces} is obtained, which viewed as generalization cl...

2017
James L. Rovnyak Lev A. Sakhnovich J. ROVNYAK L. A. SAKHNOVICH

The Krĕın-Langer integral representation of a matrix-valued generalized Nevanlinna function arises in problems of spectral theory and interpolation. A version of this formula which is suitable for such problems, and a corresponding Stieltjes inversion formula, are derived. Some classes of generalized Nevanlinna functions which are defined in terms of behavior at infinity are characterized in te...

2005
R. G. Halburd R. J. Korhonen

Certain estimates involving the derivative f 7→ f ′ of a meromorphic function play key roles in the construction and applications of classical Nevanlinna theory. The purpose of this study is to extend the usual Nevanlinna theory to a theory for the exact difference f 7→ ∆f = f(z+ c)− f(z). An a-point of a meromorphic function f is said to be c-paired at z ∈ C if f(z) = a = f(z+c) for a fixed co...

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of mero...

2001
Seiki Mori

This is a summary report of my recent articles. Nevanlinna theory asserts that each meromorphic mapping f of C into P(C) has few defects. However, it seems that meromorphic mappings with defects are very few. In this report, we shall show that for any given transcendental meromorphic mapping of C into P(C); there is a small deformation of f which has no Nevanlinna deficient hyperplanes in Pn(C)...

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