The main goal of the paper is to investigate the hypoellipticity and the solvability in the Schwartz space S(ℝ2) and the Gelfand–Shilov spaces Sμμ(ℝ2), μ ≥ 1/2, of classes of second order Shubin type operators which generalize the twisted Laplacian. Our approach is based on the reduction to global normal forms by means of Fourier integral operators with quadratic phase functions. We describe completely the spectral properties of the original operators. The regularity/solvability results are shown by using the discrete representation of the action of Shubin operators and the characterization of S(ℝ2) and Sμμ(ℝ2) by means of eigenfunction expansions.
Hypoellipticity and Solvability in Gelfand-Shilov spcaes for twisted laplacian type operators
Gramchev T;TRANQUILLI, GIORGIA
2014-01-01
Abstract
The main goal of the paper is to investigate the hypoellipticity and the solvability in the Schwartz space S(ℝ2) and the Gelfand–Shilov spaces Sμμ(ℝ2), μ ≥ 1/2, of classes of second order Shubin type operators which generalize the twisted Laplacian. Our approach is based on the reduction to global normal forms by means of Fourier integral operators with quadratic phase functions. We describe completely the spectral properties of the original operators. The regularity/solvability results are shown by using the discrete representation of the action of Shubin operators and the characterization of S(ℝ2) and Sμμ(ℝ2) by means of eigenfunction expansions.
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