Partial Fourier series on compact Lie groups

Abstract

In this note we investigate the partial Fourier series on a product of two compact Lie groups. We give necessary and sufficient conditions for a sequence of partial Fourier coefficients to define a smooth function or a distribution. As applications, we will study conditions for the global solvability of an evolution equation defined on ${\mathbb{T}}^1\times {\mathbb{S}}^3$ and we will show that some properties of this evolution equation can be obtained from a constant coefficient equation.

arXiv comment21 pages

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Cited by in corpus (6)

• Global hypoellipticity and global solvability for vector fields on compact Lie groups
• Global analytic hypoellipticity for a class of evolution operators on ${\mathbb{T}}^1\times {\mathbb{S}}^3$
• Regularity of solutions to a Vekua-type equation on compact Lie groups
• Global solutions for systems of strongly invariant operators on closed manifolds
• Global properties of vector fields on compact Lie groups in Komatsu classes. II. Normal forms
• Solvability of Vekua-type periodic operators and applications to classical equations