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<p>It is well known that every white noise operator admits an infinite series expansion in terms of integral kernel operators and, therefore, is considered as a function of the annihilation operator and creation operator. This gives a natural idea for studying the quantum white noise counterpart of the Tricomi equation by replacing the real variables <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4646_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>x</mi> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4646_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(y\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>y</mi> </math></EquationSource> </InlineEquation> by the non-commutative variables annihilation operator and creation operator. Based on an infinite-dimensional test space of holomorphic functions, the solutions are shown to be linear continuous operators.</p>

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Quantum white noise Tricomi equation

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Hafedh Rguigui

摘要

It is well known that every white noise operator admits an infinite series expansion in terms of integral kernel operators and, therefore, is considered as a function of the annihilation operator and creation operator. This gives a natural idea for studying the quantum white noise counterpart of the Tricomi equation by replacing the real variables \(x\) x and \(y\) y by the non-commutative variables annihilation operator and creation operator. Based on an infinite-dimensional test space of holomorphic functions, the solutions are shown to be linear continuous operators.