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June 8, 2026Open Access

Spectral Normalization and the Emergence of a Computational Boundary in Elliptic Operators

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Authors

AKAleš Kováč

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Overview

Analytical and numerical examples reveal spectral boundaries in elliptic operators, suggesting new applications.

Key Points

  • This work aims to define the spectral horizon and investigate its implications for elliptic operators.
  • Analyzed a one-dimensional example of the Laplace operator with Dirichlet boundary conditions.
  • Demonstrated a two-dimensional numerical example on a domain with an interior circular hole.
  • Discussed robustness under scaling, geometric deformation, and discretization.
  • Normalized spectral radius produced a dimensionless spectrum within (0,1] with 1 as the reachability limit.
  • The concept of the spectral horizon was observed in varied geometries beyond one dimension.
  • Provided a formal foundation for computational boundaries in spectral problems.

Cite This Study

Aleš Kováč (2026) studied this question.

synapsesocial.com/papers/6a265ccbad53cfb9357c5fadhttps://doi.org/10.5281/zenodo.20574485
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