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Spectral multipliers for functions of fixed $K$-type on $L^p(SL(2,\mathbb{R}))$ (1809.09385v1)
Published 25 Sep 2018 in math.FA, math.RT, and math.SP
Abstract: We prove an $Lp$ spectral multiplier theorem for functions of the $K$-invariant sublaplacian $L$ acting on the space of functions of fixed $K$-type on the group $SL(2,\mathbb{R}).$ As an application we compute the joint $Lp(SL(2,\mathbb{R}))$ spectrum of $L$ and the derivative along $K$.
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