Inversin of double Fourier integral of non-Lebesgue integrable bounded variation functions

• DOI: 10.48550/arxiv.2405.12499
• Publication Date: 2024-05-21
• Authors: Edgar Torres-Teutle; Francisco J. Mend...; Maria G. Morales-...
• Keywords: Bounded variation; Variation (astronomy); Lebesgue's number lemma; Locally integrable function

This work proves pointwise convergence of the truncated Fourier double integral non-Lebesgue integrable bounded variation functions. leads to Dirichlet-Jordan theorem proof for functions, which has not been sufficiently studied. Note that recent contributions regarding this subject consider Lebesgue [F. Moricz, 2015], [B. Ghodadra-V. Fuulop, 2016].