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• W3044254167 abstract "For <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>s</mml:mi><mml:mo>∈</mml:mo><mml:mi>ℝ</mml:mi><mml:mo>,</mml:mo></mml:math> denote by <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup><mml:mi>f</mml:mi></mml:math> the “projection” of a function <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mi>f</mml:mi></mml:math> in <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mi mathvariant=script>D</mml:mi><mml:mfenced open=( close=)><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:math> into the eigenspaces of the Dunkl Laplacian <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:msub><mml:mrow><mml:mi>Δ</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub></mml:math> corresponding to the eigenvalue <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mo>−</mml:mo><mml:msup><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>.</mml:mo></mml:math> The parameter <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mi>k</mml:mi></mml:math> comes from Dunkl’s theory of differential-difference operators. We shall characterize the range of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:msubsup><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msubsup></mml:math> on the space of functions <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant=script>D</mml:mi><mml:mfenced open=( close=)><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:mfenced></mml:math> supported inside the closed ball <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M10><mml:mover accent=false><mml:mrow><mml:mi>B</mml:mi><mml:mfenced open=( close=)><mml:mrow><mml:mi>O</mml:mi><mml:mo>,</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mrow><mml:mo stretchy=true>¯</mml:mo></mml:mrow></mml:mover><mml:mo>.</mml:mo></mml:math> As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform." @default.
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• W3044254167 date "2020-07-24" @default.
• W3044254167 modified "2023-09-24" @default.
• W3044254167 title "The Range of the Spectral Projection Associated with the Dunkl Laplacian" @default.
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• W3044254167 doi "https://doi.org/10.1155/2020/7803719" @default.
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