<p>The Maslov–Heaviside method is applied to the inversion of a polynomial operator by the Maslov–Chebyshev symbol introduced in the paper. The result is applied to the proof of a theorem on the Bessel operator in the Stepanov spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7887_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">$S_p(\mathbb {R}^n),$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>S</mi> <mi>p</mi> </msub> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7887_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="86" /> </InlineMediaObject> <EquationSource Format="TEX">$1<p<\infty ,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo><</mo> <mi>p</mi> <mo><</mo> <mi>∞</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7887_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="92" /> </InlineMediaObject> <EquationSource Format="TEX">$n=1,2,\dots .$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>.</mo> </mrow> </math></EquationSource> </InlineEquation> This significantly expands the scope of application of operator methods to the study of the correct solvability of equations with the Laplace operator usually studied in <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7887_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$L_p$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>p</mi> </msub> </math></EquationSource> </InlineEquation> spaces.</p>

INVERSION OF A POLYNOMIAL OPERATOR WITH THE MASLOV–CHEBYSHEV SYMBOL

期刊论文
发表日期：

2025年7月1日

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A. V. Kostin

摘要

The Maslov–Heaviside method is applied to the inversion of a polynomial operator by the Maslov–Chebyshev symbol introduced in the paper. The result is applied to the proof of a theorem on the Bessel operator in the Stepanov spaces $S_p(\mathbb {R}^n),$ $S_{p} (R^{n}),$ $1<p<\infty ,$ $1 < p < \infty,$ $n=1,2,\dots .$ $n = 1, 2, \dots .$ This significantly expands the scope of application of operator methods to the study of the correct solvability of equations with the Laplace operator usually studied in $L_p$ $L_{p}$ spaces.