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August 6, 2026Open Access

On a Class of Infinite Hermitised Toeplitz-Catalan Operators and Their Bounded Spectral Properties

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Authors

YYYOUSEF MUHAMMAD ALSAGHIR Al YOUSEF

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Implication

Randomized trial reveals bounded spectral properties in Toeplitz operators, suggesting new insights into the Riemann zeta function.

Key Points

  • This research aims to develop a framework connecting combinatorial structures and spectral geometry through a new class of operators.
  • Introduced a class of infinite dense convolution Toeplitz operators involving Catalan numbers.
  • Applied diagonal expansion and the Bounded Extension Theorem to establish properties of the operators.
  • Examined the critical line using complex extension and spectral trace minimization.
  • Proved Hilbert-Schmidt compactness, finiteness, and self-adjointness of operator T.
  • Demonstrated that non-trivial zeros are spectral invariants required to be on the critical line.
  • Showed that any deviation from the critical line leads to energy deficits, contradicting required statistical properties.

Cite This Study

YOUSEF MUHAMMAD ALSAGHIR Al YOUSEF (2026) studied this question.

synapsesocial.com/papers/6a7437ba764cddc9499d54a2https://doi.org/10.5281/zenodo.21790800
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