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generalized Weyl derivative

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    A Spectral Algebra for Multidimensional Weyl Fractional Operators on Exponential Characters

    by Ariel Daley
    17 views

    Abstract. Let \(d\in\mathbb{N}\). We show that multidimensional Weyl fractional operators admit a natural spectral realization on the algebraic span of exponential characters. More precisely, if \(\Lambda\subset (\mathbb{C}_+)^d\) and \[ e_\lambda(x):=e^{\langle \lambda,x\rangle}, \qquad \lambda\in\Lambda,\ x\in\mathbb{R}^d, \] where \(\mathbb{C}_+:=\{z\in\mathbb{C}:\Re z>0\}\), then the algebraic direct sum \[ \mathcal{E}_{\Lambda}^{\mathrm{alg}} := \bigoplus_{\lambda\in\Lambda}\mathbb{C}e_\lambda \] carries a …

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