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<p>We consider the sampling problem for two-sided small Fock spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {F}^p_{\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mrow> <mi mathvariant="script">F</mi> </mrow> <mi>α</mi> <mi>p</mi> </msubsup> </math></EquationSource> </InlineEquation>, for the full range <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(0 &lt; p \leqslant \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>&lt;</mo> <mi>p</mi> <mo>⩽</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. We establish a geometric description of shift-invariant sampling sequences, i.e., sequences <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Λ</mi> </math></EquationSource> </InlineEquation> such that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(c \Lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mi mathvariant="normal">Λ</mi> </mrow> </math></EquationSource> </InlineEquation> is sampling for all <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(c \in \mathbb {C} \setminus \{ 0 \}.\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>c</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mo stretchy="false">{</mo> <mn>0</mn> <mo stretchy="false">}</mo> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation></p>

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Shift-invariant sampling in two-sided small Fock spaces

  • 期刊论文

  • 发表日期：

    2026年5月21日

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  • Yurii Belov,
  • Mikhail Mironov

摘要

We consider the sampling problem for two-sided small Fock spaces \(\mathcal {F}^p_{\alpha }\) F α p , for the full range \(0 < p \leqslant \infty \) 0 < p ⩽ ∞ . We establish a geometric description of shift-invariant sampling sequences, i.e., sequences \(\Lambda \) Λ such that \(c \Lambda \) c Λ is sampling for all \(c \in \mathbb {C} \setminus \{ 0 \}.\) c ∈ C \ { 0 } .