Desirable Decompositions of Generalized Nevanlinna Functions

2014/12/31 by Muhamed Borogovac, Borogovac, Muhamed
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Stability and Controllability of Differential Equations #math.FA

paper · pdf · doi:10.48550/arxiv.1501.00214

16 pages

openalex publication_date 2014/12/31 · arxiv created 2015/02/27 · arxiv updated 2015/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a given generalized Nevanlinna function Q∈ N_κ( H ), we study decompositions that satisfy: Q=Q₁+Q₂; Q_i∈ N_κ_i( H ), and κ₁+κ₂=κ, 0≤ κ_i, which we call desirable decompositions. In this paper, some sufficient conditions for such decompositions of Q are given. One of the main results is a new operator representation of Q(z):=-Q(z)^-1 if Q( z ):=Γ₀⁺( A-z)^-1Γ₀, where A is a bounded self-adjoint operator in a Pontryagin space. The new representation is used to get an interesting desirable decomposition of Q and to obtain some information about singularities of Q.

Citations

• Characterizations of generalized poles by pole cancellation functions of higher order

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