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<p>In this paper, we introduce the integro-differential operators of infinite-order related to index Kontorovich-Lebedev transform (KL-transform) over weighted Lebesgue spaces. We derive some of these operator’s properties. In addition, we determine the necessary and sufficient conditions under which a class of integro-differential operators of infinite-order is unitary on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}(\mathbb {R}^{+};~4{\pi }^{2} x\,dx)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mo>+</mo> </msup> <mo>;</mo> <mspace width="3.33333pt" /> <mn>4</mn> <msup> <mrow> <mi>π</mi> </mrow> <mn>2</mn> </msup> <mi>x</mi> <mspace width="0.166667em" /> <mi>d</mi> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. At the end, certain classes that are related to integro-differential equations are examined.</p>

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THE INTEGRO-DIFFERENTIAL OPERATORS ON THE POSITIVE HALF LINE OF INFINITE-ORDER RELATED TO A VARIANT OF THE KONTOROVICH-LEBEDEV TRANSFORM

  • 期刊论文

  • 发表日期：

    2026年2月8日

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  • Praveen Kumar,
  • Jeetendrasingh Maan,
  • Ramesh Kumar Vats

摘要

In this paper, we introduce the integro-differential operators of infinite-order related to index Kontorovich-Lebedev transform (KL-transform) over weighted Lebesgue spaces. We derive some of these operator’s properties. In addition, we determine the necessary and sufficient conditions under which a class of integro-differential operators of infinite-order is unitary on \(L^{2}(\mathbb {R}^{+};~4{\pi }^{2} x\,dx)\) L 2 ( R + ; 4 π 2 x d x ) . At the end, certain classes that are related to integro-differential equations are examined.