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This is a survey of recent advances in harmonic analysis on the group \(\mathrm {SL}(2,\mathbb {R})\) . We will focus on the Wiener-Tauberian theorem, originally formulated for functions in the Euclidean setting, which encounters challenges when extended to noncompact semisimple Lie groups. Additionally, we will discuss multiplier operators, examining their boundedness on various spaces, and for each Fourier matrix coefficient on the group \(\mathrm {SL}(2,\mathbb {R})\) . This note is based on the article by the author (Forum Math. 33(1):213–243, 2021) and a forthcoming article (preprint 2024) co-authored with Vishvesh Kumar and Michael Ruzhansky.

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Recent Advances in Harmonic Analysis on the Group \(\mathrm {SL}(2,\mathbb {R})\)

  • 会议论文

  • 发表日期：

    2025年

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  • Tapendu Rana

摘要

This is a survey of recent advances in harmonic analysis on the group \(\mathrm {SL}(2,\mathbb {R})\) . We will focus on the Wiener-Tauberian theorem, originally formulated for functions in the Euclidean setting, which encounters challenges when extended to noncompact semisimple Lie groups. Additionally, we will discuss multiplier operators, examining their boundedness on various spaces, and for each Fourier matrix coefficient on the group \(\mathrm {SL}(2,\mathbb {R})\) . This note is based on the article by the author (Forum Math. 33(1):213–243, 2021) and a forthcoming article (preprint 2024) co-authored with Vishvesh Kumar and Michael Ruzhansky.