Abstract
In this paper we characterise ther-nuclearity of Fourier integraloperators on Lebesgue spaces. Fourier integral operators will be consideredinRn,the discrete groupZn,then-dimensional torus and symmetric spaces(compact homogeneous manifolds). We also give formulae forthe nucleartrace of these operators. Explicit examples will be given onZn,the torusTn,the special unitary group SU(2),and the projective complex planeCP2.Ourmain theorems will be applied to the characterization ofr-nuclear pseudo-differential operators defined by the Weyl quantization procedure.
Highlights
In this paper we characterise the r-nuclearity of Fourier integral operators on Lebesgue spaces
Fourier integral operators will be considered in Rn, the discrete group Zn, the n-dimensional torus and symmetric spaces
We give formulae for the nuclear trace of these operators
Summary
In this paper we characterise the r-nuclearity of Fourier integral operators on Lebesgue spaces. Fourier integral operators will be considered in Rn, the discrete group Zn, the n-dimensional torus and symmetric spaces (compact homogeneous manifolds). We give formulae for the nuclear trace of these operators. Explicit examples will be given on Zn, the torus Tn, the special unitary group SU(2), and the projective complex plane CP2. Our main theorems will be applied to the characterization of r-nuclear pseudo-differential operators defined by the Weyl quantization procedure
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