Immersion of the Fourier transform in a continuous group of functional transformations
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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.
“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]
The passage labeled Abstract (page unavailable) describes a continuous group of transformations containing the ordinary Fourier transform, supporting the idea of fractional Fourier transforms. The paper is dated 1937, and our copy does not establish that the idea appeared as early as 1929 (searched: “1929” and “fractional powers”). (LLM, conf=0.88)
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- 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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