Dissipation and c-Entropy in Nevanlinna-Pick Interpolation
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910192612933632 |
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| author | Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard |
| author_facet | Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard |
| contents | We study interpolation L-systems realizing finite Nevanlinna-Pick data sets and analyze their structural and quantitative characteristics. Explicit formulas are derived for the c-entropy and dissipation coefficient, two intrinsic invariants that describe the dissipative structure of interpolation L-systems. These quantities depend only on the geometric placement of interpolation nodes in $\mathbb{C}_+$, attaining maximal finite values for purely imaginary nodes. The interpolation model $Θ_Δ$ and its unitary equivalents reveal that these invariants form a direct link between analytic interpolation data and the dynamical properties of L-systems. Particular attention is given to symmetric configurations, where the impedance function admits an explicit rational representation and a natural physical interpretation in terms of equivalent $LC$-networks. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04101 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dissipation and c-Entropy in Nevanlinna-Pick Interpolation Belyi, Sergey Makarov, Konstantin A. Tsekanovskii, Eduard Functional Analysis Mathematical Physics Spectral Theory Primary 47A10, Secondary 47N50, 81Q10 We study interpolation L-systems realizing finite Nevanlinna-Pick data sets and analyze their structural and quantitative characteristics. Explicit formulas are derived for the c-entropy and dissipation coefficient, two intrinsic invariants that describe the dissipative structure of interpolation L-systems. These quantities depend only on the geometric placement of interpolation nodes in $\mathbb{C}_+$, attaining maximal finite values for purely imaginary nodes. The interpolation model $Θ_Δ$ and its unitary equivalents reveal that these invariants form a direct link between analytic interpolation data and the dynamical properties of L-systems. Particular attention is given to symmetric configurations, where the impedance function admits an explicit rational representation and a natural physical interpretation in terms of equivalent $LC$-networks. |
| title | Dissipation and c-Entropy in Nevanlinna-Pick Interpolation |
| topic | Functional Analysis Mathematical Physics Spectral Theory Primary 47A10, Secondary 47N50, 81Q10 |
| url | https://arxiv.org/abs/2605.04101 |