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Immersion of the Fourier Transform in a Continuous Group of Functional Transformations
Open accessAbstract
The sequence in the regeneration of a plate row is as follows: healing, stretching of the remaining part or parts of the canal and concentration of mesogleal cells at the wound area, fusion of parts of the canal, hollowing out at the region of fusion and formation of plates above the new canal.3. Cells from the remaining part or parts of a row or from neighboring rows and also nonspecialized cells in the mesoglea take an active part in the regeneration of plate rows.4. Contracting muscle strands which are anchored to the plate row and also in the mesoglea aid in the reformation of a row following its removal in part or as a whole.
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“The idea of fractional powers of the Fourier transform operator appears in the mathematical literature as early as 1929 [23,9,11].”
From Computation of the fractional Fourier transform (2004) · cites this paper as [9]
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Fractional Fourier transform as a signal processing tool: An overview of recent developments
Sejdić, E., Djurović, I., & Stanković, L. (2010) · Signal Processing · doi:10.1016/j.sigpro.2010.10.008 · Cited by 425
The discrete fractional cosine and sine transforms
Pei, S.-C., & Yeh, M.-H. (2001) · IEEE Transactions on Signal Processing · doi:10.1109/78.923302 · Cited by 176
Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles
Alonso, M. A. (2011) · Advances in Optics and Photonics · doi:10.1364/aop.3.000272 · Cited by 178
Product and Convolution Theorems for the Fractional Fourier Transform
Almeida, L. B. (1997) · IEEE Signal Processing Letters · doi:10.1109/97.551689 · Cited by 167
introduction to the fractional fourier transform and its applications
Ozaktas, H. M., Kutay, M. A., & Mendlovic, D. (1999) · Advances in Imaging and Electron Physics · doi:10.1016/s1076-5670(08)70272-6 · Cited by 164
Metadata
- Authors
- Condon, E. U.
- Affiliations
- Princeton University (US)
- Corresponding author
- Condon, E. U.
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 1937-03
- Volume
- 23
- Issue
- 3
- Pages
- 158-164
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC1076889
- OpenAlex
- W2019388666
- Semantic Scholar
- 8645864831948046cee66f6ab9af21d755e68d47
- Cited by
- 174
- References
- 0
- Citations by year
- 2026: 4 · 2025: 5 · 2024: 6 · 2023: 3 · 2022: 7 · 2021: 6 · 2020: 7 · 2019: 8 · 2018: 8 · 2017: 11 · 2016: 10 · 2015: 5 · 2014: 7 · 2013: 5 · 2012: 7
- FWCI
- 2.31
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Operator Algebra Research
- Physical Sciences › Mathematics › Applied Mathematics › Advanced Harmonic Analysis Research
- Keywords
- Fourier transform, continuous groups, functional transformation, group theory
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