Inversion of a polynomial operator with the Maslov–Chebyshev symbol

A. V. Kostin<sup>ab

a</sup> Voronezh State University, Voronezh, Russia
^b Concern “Sozvezdie”, Voronezh, Russia

Abstract: 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 $S_p(\mathbb{R}^n),$ $1<p<\infty,$ $n=1,2,\dots.$ 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 $L_p$ spaces.

Keywords: Stepanov spaces, Bessel operator, Maxwell–Fejér operator symbol, Weierstrass semigroup, correct solvability, Chebyshev polynomials, strongly continuous semigroup, polyharmonic equation.

UDC: 517.9

DOI: 10.22363/2413-3639-2024-70-4-626-635