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- W2999668047 abstract "In this paper we develop the calculus of pseudo-differential operators on the lattice Zn, which we can call pseudo-difference operators. An interesting feature of this calculus is that the global frequency space (Tn) is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable. We establish formulae for composition, adjoint, transpose, and for parametrix for the elliptic operators. We also give conditions for the ℓ2, weighted ℓ2, and ℓp boundedness of operators and for their compactness on ℓp. We describe a link to the toroidal quantization on the torus Tn, and apply it to give conditions for the membership in Schatten classes on ℓ2(Zn). Furthermore, we discuss a version of Fourier integral operators on the lattice and give conditions for their ℓ2-boundedness. The results are applied to give estimates for solutions to difference equations on the lattice Zn. Moreover, we establish Gårding and sharp Gårding inequalities, with an application to the unique solvability of parabolic equations on the lattice Zn." @default.
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- W2999668047 date "2020-06-01" @default.
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- W2999668047 title "Difference equations and pseudo-differential operators on <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.svg><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>Z</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>" @default.
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- W2999668047 doi "https://doi.org/10.1016/j.jfa.2020.108473" @default.
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