What question did this study set out to answer?

The aim is to explore the spectral characteristics and numerical behavior of the discrete Abel integral operator.

May 6, 2026Open Access

On the Spectral Norm of the Discrete Abel Integral Operator: Numerical Convergence and the Emergence of the Ontological Conductivity Constant C∞

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OGOleg Glushkov

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Implication

This analysis demonstrates the operator norm converges numerically to the fundamental constant in spectral properties of the discrete Abel integral operator, indicating implications for resonant field

Key Points

The aim is to explore the spectral characteristics and numerical behavior of the discrete Abel integral operator.
Investigated the spectral properties of the symmetric Abel integral operator on L2[0, 1] using numerical methods.
Utilized high-precision numerical discretization and finite-size scaling.
Analyzed the convergence of the operator norm for an N × N quadrature discretization.
Identified a fundamental constant C∞ approximately equal to 2.6828.
Demonstrated operator norm converges according to the relation ∥TN∥ ∼ C∞√N.
Proposed the fundamental constant as an invariant relating to embedded field structures.

Cite This Study

Oleg Glushkov (2026) studied this question.

synapsesocial.com/papers/69faa2e204f884e66b533736 https://doi.org/10.5281/zenodo.20030699

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On the Spectral Norm of the Discrete Abel Integral Operator: Numerical Convergence and the Emergence of the Ontological Conductivity Constant C∞

Discussion

Member takes

Implication

Key Points

Cite This Study

On the Spectral Norm of the Discrete Abel Integral Operator: Numerical Convergence and the Emergence of the Ontological Conductivity Constant C∞

Discussion

Member takes

Implication

Key Points

Cite This Study

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