@inproceedings{91da3b1e3a1f430c97f8a47ca4b21910,
title = "Perturbed Fourier Transform Associated with Schr{\"o}dinger Operators",
abstract = "We give an exposition on the L2 theory of the perturbed Fourier transform associated with a Schr{\"o}dinger operator H=−d2∕dx2+V on the real line, where V is a real-valued finite measure. In the case V L1∩L2, we explicitly define the perturbed Fourier transform for H and obtain an eigenfunction expansion theorem for square integrable functions. This provides a complete proof of the inversion formula for that covers the class of short range potentials in (Forumala Presented). Such paradigm has applications in the study of scattering problems in connection with the spectral properties and asymptotic completeness of the wave operators.",
keywords = "Scattering, Schr{\"o}dinger operator, Spectral theory",
author = "Shijun Zheng",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.; 1st Southern Georgia Mathematics Conference, SGMC 2021 ; Conference date: 02-04-2021 Through 03-04-2021",
year = "2024",
doi = "10.1007/978-3-031-69706-7_2",
language = "English",
isbn = "9783031697050",
series = "Springer Proceedings in Mathematics and Statistics",
publisher = "Springer",
pages = "25--71",
editor = "Divine Wanduku and Shijun Zheng and Zhan Chen and Andrew Sills and Haomin Zhou and Ephraim Agyingi",
booktitle = "Applied Mathematical Analysis and Computations I - 1st SGMC",
address = "Germany",
}