Scholarlink

<p>We characterize the inverse of an analytic Fredholm operator-valued function <i>A</i>(<i>z</i>) near an isolated singularity within a general Banach space framework. Our approach relies on the sequential factorization of <i>A</i>(<i>z</i>) via Fredholm quotient operators. By analyzing the properties of these quotient operators near <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(z=z_0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>=</mo> <msub> <mi>z</mi> <mn>0</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, we fully characterize the Laurent series expansion of the inverse of <i>A</i>(<i>z</i>) in terms of its Taylor coefficients around the singularity. These theoretical results are subsequently applied to characterize the solution of a general autoregressive law of motion in a Banach space.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Inversion of An Analytic Operator Function Through Fredholm Quotients and its Application

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月15日

查看全文
  • Won-Ki Seo

摘要

We characterize the inverse of an analytic Fredholm operator-valued function A(z) near an isolated singularity within a general Banach space framework. Our approach relies on the sequential factorization of A(z) via Fredholm quotient operators. By analyzing the properties of these quotient operators near \(z=z_0\) z = z 0 , we fully characterize the Laurent series expansion of the inverse of A(z) in terms of its Taylor coefficients around the singularity. These theoretical results are subsequently applied to characterize the solution of a general autoregressive law of motion in a Banach space.