Journal of Functional Analysis· 2026Q1
Fourier transform of BV functions and applications
- 1citations
- Q1SCImago
- 2026year
Short summary
A new weighted Plancherel identity for BV functions is derived, linking their Fourier transform to their L2-jump product, which leads to a characterization of sets of finite perimeter via their Fourier transform.
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Key points
- Introduced L2-jump product for BV functions.
- Derived a weighted Plancherel identity for BV functions.
- Characterized sets of finite perimeter using their Fourier transform.
- Generalized Beck and Montgomery's estimates for quadratic discrepancy.
AI-generated from the title and abstract; the full text is not read.
Abstract
This paper investigates the relation between the Fourier transform of BV (bounded variation) functions and their jump sets. We introduce the notion of L 2 -jump product and obtain a weighted Plancherel identity for BV functions. As a corollary, we get a characterization of sets of finite perimeter in terms of their Fourier transform. Moreover, we sharpen a result of Herz on the set-theoretic derivative of the Fourier transform of characteristic functions of sets. Last, we obtain sharp bounds on the quadratic discrepancy of BV functions, and as a consequence, we generalize the classic estimates of Beck and Montgomery.
The authors' abstract, as published at the source. Journal of Functional Analysis, 2026 · DOI ↗
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