In this thesis, we investigate a collection of extremal problems centered on the interplay between a function and its Fourier transform. A recurring theme is the study of constraints imposed simultaneously on both a function and its Fourier transform, and the sharp inequalities and rigidity phenomena that arise from such conditions. We also explore applications of some of these extremal problems to questions in analytic number theory.
Extremal Problems in Fourier Analysis and Applications to Number Theory / Ismoilov, T.I.U.. - (2026 Sep 08).
Extremal Problems in Fourier Analysis and Applications to Number Theory
ISMOILOV, TOLIBJON IKROMBOY UGLI
2026-09-08
Abstract
In this thesis, we investigate a collection of extremal problems centered on the interplay between a function and its Fourier transform. A recurring theme is the study of constraints imposed simultaneously on both a function and its Fourier transform, and the sharp inequalities and rigidity phenomena that arise from such conditions. We also explore applications of some of these extremal problems to questions in analytic number theory.File in questo prodotto:
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Extremal Problems in Fourier Analysisand Applications to Number Theory.pdf
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Descrizione: tesi di Ph.D.
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Tesi
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