<p>In this article, we investigate the existence of Riesz bases (RB) under multi-subordinate perturbations. We apply these theoretical results to the analysis of block matrices composed of linear operators. Additionally, we consider infinite series of perturbed operators of the form: <Equation ID="Equ9"> <EquationSource Format="TEX">$ \sum _{k=0}^{\infty } \omega ^k \mathcal {T}_k \zeta , \quad \forall \zeta \in {D}(\mathcal {T}_0), $</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <munderover> <mo>∑</mo> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>∞</mi> </munderover> <msup> <mi>ω</mi> <mi>k</mi> </msup> <msub> <mi mathvariant="script">T</mi> <mi>k</mi> </msub> <mi>ζ</mi> <mo>,</mo> <mspace width="1em" /> <mo>∀</mo> <mi>ζ</mi> <mo>∈</mo> <mi>D</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="script">T</mi> <mn>0</mn> </msub> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </Equation>where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\omega \in \mathbb {C}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> </mrow> </math></EquationSource> </InlineEquation> and each <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {T}_k$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">T</mi> <mi>k</mi> </msub> </math></EquationSource> </InlineEquation> satisfies certain subordination conditions. The main motivation for this work is the spectral analysis of Gribov-type operators acting in the Bargmann space, which are closely related to high-energy quantum field models.</p>

Riesz bases for multi-subordinate perturbations with application to a Gribov operator in Bargmann space

期刊论文
发表日期：

2026年6月26日

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Abdessattar Lafi,
Olfa Messaoud

摘要

In this article, we investigate the existence of Riesz bases (RB) under multi-subordinate perturbations. We apply these theoretical results to the analysis of block matrices composed of linear operators. Additionally, we consider infinite series of perturbed operators of the form: $ \sum _{k=0}^{\infty } \omega ^k \mathcal {T}_k \zeta , \quad \forall \zeta \in {D}(\mathcal {T}_0), $ $\sum_{k = 0}^{\infty} ω^{k} T_{k} ζ, \forall ζ \in D (T_{0}),$ where $\omega \in \mathbb {C}$ $ω \in C$ and each $\mathcal {T}_k$ $T_{k}$ satisfies certain subordination conditions. The main motivation for this work is the spectral analysis of Gribov-type operators acting in the Bargmann space, which are closely related to high-energy quantum field models.