Fourier transform inversion: bounded variation, polynomial growth, Henstock-Stieltjes integration

DOI10.1515/MS-2023-0013MaRDI QIDQ2685890

Erik O.Talvila

Publication date: 23 February 2023

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.13942

zbMATH Keywords

Fourier transformdistributioncontour integralbounded variationinversionintegration by partsHenstock-Stieltjes integralheaviside step functionprincipal value

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Denjoy and Perron integrals, other special integrals (26A39)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Functions of bounded variation and their Fourier transforms
• The Fourier transform of a function of bounded variation: symmetry and asymmetry
• Pointwise behavior of Fourier integrals of functions of bounded variation over \(\mathbb R\)
• Fourier transforms in the ``classical sense, Schur spaces and a new formula for the Fourier transforms of slowly increasing, \(O(p,q)\)-invariant functions
• Fourier and wavelet analysis
• On the norm continuity of the HK-Fourier transform
• An asymptotic analysis of the Fourier-Laplace transforms of certain oscillatory functions
• Distributional point values and convergence of Fourier series and integrals
• Distributional versions of littlewood’s Tauberian theorem
• A Short Proof of a Classical Theorem in the Theory of Fourier Integrals
• Recent contributions to the theory of non-absolutely convergent fourier transforms
• Kurzweil–Stieltjes Integral
• Fourier Transform Inversion Using an Elementary Differential Equation and a Contour Integral
• Bounded Variation and Around

This page was built for publication: Fourier transform inversion: bounded variation, polynomial growth, Henstock-Stieltjes integration