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<p>The resolvent set and the essential spectrum of the pseudo-differential operator are investigated by exploiting the theory of the Weinstein transform. A connection between <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> multiplier and spectral theory is given and applications related to the essential spectrum of the pseudo-differential operator involving the Weinstein transform in the Sobolev space are described.</p>

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On the essential spectrum of the pseudo-differential operator involving the Weinstein transform

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Anusuiya Yadav,
  • Santosh Kumar Upadhyay

摘要

The resolvent set and the essential spectrum of the pseudo-differential operator are investigated by exploiting the theory of the Weinstein transform. A connection between \(L^{p}\) L p multiplier and spectral theory is given and applications related to the essential spectrum of the pseudo-differential operator involving the Weinstein transform in the Sobolev space are described.