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Spectral synthesis and partial differential equations

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We offer a new approach to spectral synthesis on affine groups. The idea is to consider solution spaces of systems of linear partial differential equations corresponding to invariant differential operators with respect to some closed subgroup of the general linear group on \(\mathbb{R}^n\). We show that a certain type of spherical spectral analysis and spectral synthesis holds for such solution spaces.

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Correspondence to L. Székelyhidi.

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The research was partly supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. K11165.

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Székelyhidi, L. Spectral synthesis and partial differential equations. Acta Math. Hungar. 161, 31–47 (2020).

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