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Non Commutative Fourier Duality on one-Dimension and its Applications
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The present article aims to present an extension of the Fourier duality to non-commutative groups and algebraic structures,analyzing the non-commutative Fourier transform on one dimensional structures along with their unitary representation. This approach gives a comprehensive insight into the harmonic analysis of operator-valued functions, providing mathematical foundations for analyzing physical systems that exhibit non-commutative symmetries. Hence the article discusses applications of non-commutative harmonic analysis into emerging fields of physics such as quantum mechanics and models of quantum gravity , opening paths for exploration of the connections between non-commutative algebras, harmonic analysis, and theoretical Physics.
Title: Non Commutative Fourier Duality on one-Dimension and its Applications
Description:
The present article aims to present an extension of the Fourier duality to non-commutative groups and algebraic structures,analyzing the non-commutative Fourier transform on one dimensional structures along with their unitary representation.
This approach gives a comprehensive insight into the harmonic analysis of operator-valued functions, providing mathematical foundations for analyzing physical systems that exhibit non-commutative symmetries.
Hence the article discusses applications of non-commutative harmonic analysis into emerging fields of physics such as quantum mechanics and models of quantum gravity , opening paths for exploration of the connections between non-commutative algebras, harmonic analysis, and theoretical Physics.
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