WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES
Abstract
Weighted Reproducing Kernel Banach Spaces (WRKBS) extend kernel theory by incorporating weights to enhance modeling flexibility. This paper defines WRKBS, explores their theoretical foundations, and demonstrates their effectiveness in regression, classification, and clustering. Numerical experiments validate their advantages in structured data modeling and symmetry-aware learning. Applications span computer vision, physics-based modeling, and graph-based learning, with future directions in scalable algorithms and deep learning integration.
Keywords
Ethical Statement
The authors declare that the work presented in this manuscript is original and has not been published previously. All authors have read and approved the final version of the manuscript and have agreed to its submission to this journal. There are no conflicts of interest, financial or otherwise, associated with this work. Any sources of funding or support have been appropriately acknowledged within the manuscript.
References
- Agud, L., Calabuig, J. M., (2020), Weighted p-regular kernels for reproducing kernel Hilbert spaces and Mercer Theorem, J. Anal. Appl, 18 (3), pp. 359–383.
- Alpay, D., (2012), Reproducing kernel spaces and applications, Springer.
- Bartolucci, F., De Vito, E., Rosasco, L., (2024), Neural reproducing kernel Banach spaces and representer theorems for deep networks. arXiv:2403.08750.
- Berlinet, A., Thomas-Agnan, C., (2011), Reproducing kernel Hilbert spaces in probability and statistics, Springer.
- Bonet, J., (2022), Weighted Banach spaces of analytic functions with sup-norms and operators, RACSAM, 116, Article 184.
- Cheng, R., Mashreghi, J., Ross, W. T., (2019), Inner functions in reproducing kernel spaces, Springer.
- Colonna, F., Tjani, M., (2015), Essential norms of weighted composition operators from reproducing kernel Hilbert spaces into weighted-type spaces. Mediterr J Math, 12, pp. 1357–1375.
- Giannakis, D., Montgomery, M., (2024), An algebra structure for reproducing kernel Hilbert spaces. arXiv:2401.01295.
Details
Primary Language
English
Subjects
Operator Algebras and Functional Analysis
Journal Section
Research Article
Publication Date
December 6, 2025
Submission Date
December 12, 2024
Acceptance Date
April 25, 2025
Published in Issue
Year 2025 Volume: 15 Number: 12
APA
Hashemi Sababe, S., & Biranvand, N. (2025). WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES. TWMS Journal of Applied and Engineering Mathematics, 15(12), 2809-2827. https://izlik.org/JA35XY87KH
AMA
1.Hashemi Sababe S, Biranvand N. WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES. JAEM. 2025;15(12):2809-2827. https://izlik.org/JA35XY87KH
Chicago
Hashemi Sababe, Saeed, and Nader Biranvand. 2025. “WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES”. TWMS Journal of Applied and Engineering Mathematics 15 (12): 2809-27. https://izlik.org/JA35XY87KH.
EndNote
Hashemi Sababe S, Biranvand N (December 1, 2025) WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES. TWMS Journal of Applied and Engineering Mathematics 15 12 2809–2827.
IEEE
[1]S. Hashemi Sababe and N. Biranvand, “WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES”, JAEM, vol. 15, no. 12, pp. 2809–2827, Dec. 2025, [Online]. Available: https://izlik.org/JA35XY87KH
ISNAD
Hashemi Sababe, Saeed - Biranvand, Nader. “WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES”. TWMS Journal of Applied and Engineering Mathematics 15/12 (December 1, 2025): 2809-2827. https://izlik.org/JA35XY87KH.
JAMA
1.Hashemi Sababe S, Biranvand N. WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES. JAEM. 2025;15:2809–2827.
MLA
Hashemi Sababe, Saeed, and Nader Biranvand. “WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 12, Dec. 2025, pp. 2809-27, https://izlik.org/JA35XY87KH.
Vancouver
1.Saeed Hashemi Sababe, Nader Biranvand. WEIGHTED REPRODUCING KERNEL PROPERTY ON BANACH SPACES. JAEM [Internet]. 2025 Dec. 1;15(12):2809-27. Available from: https://izlik.org/JA35XY87KH