Skip to content
DraconiticResearch
Search Sources API
179,152 studies31 sourcesUpdated 6 min ago
PreprintarXiv licencearXiv

The Taylor Integral and a Generalization of the Discrete Fourier Transform

  • Athanasios Christou Micheas
Open at sourcePDFDOICite

Abstract

We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the discrete Fourier transform, and we identify general conditions for it to be invertible when applied to any real or complex sequence. Applications to the mathematical sciences are also presented.

Related

  1. FASS: Discrete Fourier Transform Adapters for Speech Separation With Incremental Learning
    Ziye Yang, Xiang Song, Min Zhao +3
    IEEE Transactions on Audio, Speech and Language ProcessingPeer-reviewedPublisher termsFull textStatisticsHAL
  2. Contour-integral and Fourier transform based multivariable quantum eigenvalue transformation for commuting matrices
    Shan Jiang, Dong An
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingQuantum physics & quantum informationarXiv
  3. Approximate Inversion of Discrete Fourier Integral Operators via Hierarchically Semiseparable Matrices
    Yingzhou Li, Jingyu Liu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. A Superfast Direct Solver for 2D Type-II Inverse Nonuniform Discrete Fourier Transform Based on Hierarchically Semiseparable Matrices
    Yingzhou Li, Jingyu Liu
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  5. A Diophantine generalization of Fourier's irrationality trick
    Archan Chattopadhyay, Chandan Chattopadhyay
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{micheas2026taylor,
  title = {{The Taylor Integral and a Generalization of the Discrete Fourier Transform}},
  author = {Athanasios Christou Micheas},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2605.06706},
  eprint = {2605.06706},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.06706},
}
RIS
TY  - UNPB
TI  - The Taylor Integral and a Generalization of the Discrete Fourier Transform
AU  - Athanasios Christou Micheas
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2605.06706
UR  - https://arxiv.org/abs/2605.06706
AB  - We propose a new integral based on Taylor measures, study its properties extensively, and we illustrate that it includes many concepts from mathematics as special cases. In particular, the new integral emerges as a generalization of the discrete Fourier transform, and we identify general conditions for it to be invertible when applied to any real or complex sequence. Applications to the mathematical sciences are also presented.
ER  -