"Fourier transform over Spin(4) and a global operator calculus"Kaehler, UweIn this work we construct a group Fourier transform using representations of Spin(4) and establish the calculus of left-invariant differential operators and of difference operators on the group Spin(4) . This allows us to construct a global symbol calculus of pseudo-differential operators in the sense of Ruzhansky-Turunen-Wirth on the group Spin(4). Afterwards we apply this calculus to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some where the criteria of hypoellipticity will be reduced to the problem of distance between irrational and rational numbers. |
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