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<p>We consider the Gelfand–Shilov space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S^{\psi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mi>ψ</mi> </msup> </math></EquationSource> </InlineEquation> of type <i>S</i> defined via a countable family <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> of separately radial weight functions in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathbb {R}}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. Under certain mild assumptions on <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>, the periodization operator acts continuously from <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(S^{\psi }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>S</mi> <mi>ψ</mi> </msup> </math></EquationSource> </InlineEquation> to some space of periodic ultradifferentiable Roumieu type functions. We find sufficient conditions on <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\psi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation> that guarantee the surjectivity of the periodization operator. Bibliography: 17 titles.</p>

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ON THE PERIODIZATION OPERATOR IN THE GELFAND–SHILOV SPACE OF TYPE S

  • 期刊论文

  • 发表日期：

    2026年4月23日

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  • Il’dar Musin

摘要

We consider the Gelfand–Shilov space \(S^{\psi }\) S ψ of type S defined via a countable family \(\psi \) ψ of separately radial weight functions in \({\mathbb {R}}^n\) R n . Under certain mild assumptions on \(\psi \) ψ , the periodization operator acts continuously from \(S^{\psi }\) S ψ to some space of periodic ultradifferentiable Roumieu type functions. We find sufficient conditions on \(\psi \) ψ that guarantee the surjectivity of the periodization operator. Bibliography: 17 titles.