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Bibliographic Details
Main Authors: Chino, Yuki, Kinjo, Kensaku, Oizumi, Ryo
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.11723
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Table of Contents:
  • The Riesz projection and the corresponding eigenfunction of a positive operator satisfying the Doeblin condition are explicitly constructed using the partial Bell polynomials. While classical Fredholm theory requires stringent summability conditions, such as the operator being in a Schatten class to ensure the convergence of Fredholm minors, our approach utilizes the local algebraic structure induced by the Doeblin condition. We define a scalar function $D(λ)$ whose derivative $D'(λ_0)$ at the dominant eigenvalue $λ_0$ naturally provides the normalization constant for the projection. Consequently, an explicit functional representation of the eigenfunction is obtained as a limit of a weighted ratio of the operator's kernel, bypassing the need to solve transcendental characteristic equations.