Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Muro, Masakazu

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We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.

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In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians $L_{α}$ on the spheres $S^{2 n + 1} ≃ U (n + 1) / U (n)$ . In the second part, we introduce a larger family of left-invariant sublaplacians $L_{α, β}$ on $S^{3} ≃ S U (2)$ and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.

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Tout espace de fonctions différentiables invariant sous $0 (n)$ est une algèbre de Banach. De Leeuw et Mirkil ( 13, 1963) ont classifié tous ces “rotating spaces” pour $n = 2$ . Nous obtenons ici des résultats correspondants pour $n$ arbitraire. Une classification analogue est aussi obtenue pour des espaces de fonctions différentiables sur $C^{n}$ invariants sous $U (n)$ .

Symmetries of holomorphic geometric structures on tori

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We prove that any holomorphic locally homogeneous geometric structure on a complex torus of dimension two, modelled on a complex homogeneous surface, is translation invariant. We conjecture that this result is true in any dimension. In higher dimension, we prove it for G nilpotent. We also prove that for any given complex algebraic homogeneous space (X, G), the translation invariant (X, G)-structures on tori form a union of connected components in the deformation space of (X, G)-structures. ...