22-74 Messoud Efendiev, Vitali Vougalter

Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian (194K, pdf) Nov 6, 22

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Abstract. We establish the solvability of certain linear nonhomogeneous equations and demonstrate that under reasonable technical conditions the convergence in L^2(R^d) of their right sides implies the existence and the convergence in L^2(R^d) of the solutions. In the first part of the work the equation involves the logarithmic Laplacian. In the second part we generalize the results derived by incorporating a shallow, short-range scalar potential into the problem. The argument relies on the methods of the spectral and scattering theory for the non-Fredholm Schrodinger type operators. As distinct from the preceding articles on the subject, for the operators involved in the equations the essential spectra fill the whole real line.

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