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Theory of reproducing kernels
Open accessAbstract
May 7. Difference of reproducing kernels.354 8. Product of reproducing kernels.357 9. Limits of reproducing kernels.362 10.Construction of a r.k. by resolution of identity.368 11.Operators in spaces with reproducing kernels.371 12.The reproducing kernel of a sum of two closed subspaces.375 13.Final remarks in the general theory.380 Part II.Examples.384 1.I ntroductory remarks.384 (1) Bergman's kernels.384 (2) Harmonic kernels.386 2. Comparison domains.387 3. The difference of kernels.388 4. The square of a kernel introduced by Szegö.391 5.The kernel H{z, zi) for an ellipse.393 6. Construction of H(z, z¡) for a strip.394 7. Limits of increasing sequences of kernels.396 8. Construction of reproducing kernels by the projection-formula of §12, I.
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Cited by
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Rasmussen, C. E., & Williams, C. K. I. (2005) · doi:10.7551/mitpress/3206.001.0001 · Cited by 11,705
“1 (Moore-Aronszajn theorem, Aronszajn [1950]).”
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Craven, P., & Wahba, G. (1978) · Numerische Mathematik · doi:10.1007/bf01404567 · Cited by 3,388
Quantum Machine Learning in Feature Hilbert Spaces
Schuld, M., & Killoran, N. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.040504 · Cited by 1,840
Kernel methods in system identification, machine learning and function estimation: A survey
Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., & Ljung, L. (2014) · Automatica · doi:10.1016/j.automatica.2014.01.001 · Cited by 741
Metadata
- Authors
- Aronszajn, N.
- Venue
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1950
- Volume
- 68
- Issue
- 3
- Pages
- 337-404
- ISSN
- 0002-9947 (ISSN-L)
- 1088-6850
- OpenAlex
- W1986280275
- Cited by
- 5,380
- References
- 0
- FWCI
- 10.22
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Aronszajn, N. (1950). Theory of reproducing kernels. Transactions of the American Mathematical Society. https://doi.org/10.1090/s0002-9947-1950-0051437-7
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