On Continuous Wavelet Transform of Complex Radon Measures on ℝ^d

@misc{banerjee2026continuous,
  title = {{On Continuous Wavelet Transform of Complex Radon Measures on $\mathbbR^d$}},
  author = {Tathagata Banerjee and Vaishakh Jayaprakash},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29293},
  eprint = {2610.29293},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29293},
}

TY  - UNPB
TI  - On Continuous Wavelet Transform of Complex Radon Measures on ℝ^d
AU  - Tathagata Banerjee
AU  - Vaishakh Jayaprakash
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29293
UR  - https://arxiv.org/abs/2610.29293
AB  - This paper investigates a necessary and sufficient condition for a measurable function on ℝ^× × ℝ^d to be the continuous wavelet transform of a complex Radon measure on ℝ^d under suitable regularity conditions on the wavelets. We define a new norm on the collection of such functions and show that it is isometrically isomorphic to the Banach algebra of complex Radon measures under convolution. We show a wavelet inversion formula for measures, in a restricted sense. Under additional hypothesis, we provide a reconstruction formula for the measure of closed rectangles in ℝ^d using wavelet transforms. We have included supporting examples to substantiate these assumptions.
ER  -