Abstract relative fourier transforms over canonical homogeneous spaces of semi-direct product groups with abelian normal factor
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This article is published in Journal of The Korean Mathematical Society.The article was published on 2017-01-01 and is currently open access. It has received 14 citations till now. The article focuses on the topics: Elementary abelian group & Rank of an abelian group.read more
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Abstract convolution function algebras over homogeneous spaces of compact groups
TL;DR: In this paper, a systematic study for structure of abstract Banach functions over homogeneous spaces of compact groups is presented, where the notions of convolution and involution are introduced for the Banach function spaces.
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Abstract measure algebras over homogeneous spaces of compact groups
TL;DR: In this article, a systematic study for abstract Banach measure algebras over homogeneous spaces of compact groups is presented, where H is a closed subgroup of a compact group G and G/H is the left coset spac...
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Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear PDEs
TL;DR: This work defines the homogeneous space of 3D positions and orientations R3⋊S2:=SE(3)/({0}×SO(2)) as the quotient in SE(3) and designs a specific Fourier transform for this quotient, which reduces classical analysis computations and provides an explicit algebraic spectral decomposition of the solutions.
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Abstract Poisson summation formulas over homogeneous spaces of compact groups
TL;DR: In this article, the abstract notion of Poisson summation formulas for homogeneous spaces of compact groups was introduced, and it was shown that the abstract Fourier transform over G/H satisfies a generalized version of the Weil summation formula.
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Abstract Banach Convolution Function Modules over Coset Spaces of Compact Subgroups in Locally compact Groups
TL;DR: In this article, an operator theory approach for the abstract structure of Banach function modules over coset spaces of compact subgroups is presented, where the notion of convolution left-module action is introduced.