Abstract
In the spaces L p = L p (ℝn), we study complex powers of a nonelliptic differential operator D = I +Δ x′ represented in the form of partial acoustic potentials (in the variable x′). By using the method of approximative inverse operators, we construct the inversion of the potentials A γ x ,φ with L p -densities and describe the image A γ x ,(L p ) in terms of the inverting constructions.
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Original Russian Text © D.N. Karasev, V.A. Nogin, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 10, pp. 1316–1322.
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Karasev, D.N., Nogin, V.A. Complex powers of a nonelliptic differential operator in L p -spaces. Diff Equat 49, 1282–1289 (2013). https://doi.org/10.1134/S0012266113100091
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DOI: https://doi.org/10.1134/S0012266113100091