Unbounded translation invariant operators on commutative hypergroups
- Author
- Vishvesh Kumar (UGent) , Kumar N. Shravan and Sarma Ritumoni
- Organization
- Abstract
- Let K be a commutative hypergroup. In this article, we study the unbounded translation invariant operators on L-p(K), 1 <= p <= infinity. For p is an element of {1, 2}, we characterize translation invariant operators on L-p(K) in terms of the Fourier transform. We prove an interpolation theorem for translation invariant operators on L-p(K) and we also discuss the uniqueness of the closed extension of such an operator on L-p(K). Finally, for p is an element of {1, 2}, we prove that the space of all closed translation invariant operators on L-p(K) forms a commutative algebra over the field of complex numbers. We also prove Wendel's theorem for densely defined closed linear operators on L-1(K).
- Keywords
- Unbounded multipliers, translation invariant operators, unbounded opera- tors, hypergroups, Fourier transform, MULTIPLIERS, SPACES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8669082
- MLA
- Kumar, Vishvesh, et al. “Unbounded Translation Invariant Operators on Commutative Hypergroups.” METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, vol. 25, no. 3, 2019, pp. 236–47.
- APA
- Kumar, V., N. Shravan, K., & Ritumoni, S. (2019). Unbounded translation invariant operators on commutative hypergroups. METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, 25(3), 236–247.
- Chicago author-date
- Kumar, Vishvesh, Kumar N. Shravan, and Sarma Ritumoni. 2019. “Unbounded Translation Invariant Operators on Commutative Hypergroups.” METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY 25 (3): 236–47.
- Chicago author-date (all authors)
- Kumar, Vishvesh, Kumar N. Shravan, and Sarma Ritumoni. 2019. “Unbounded Translation Invariant Operators on Commutative Hypergroups.” METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY 25 (3): 236–247.
- Vancouver
- 1.Kumar V, N. Shravan K, Ritumoni S. Unbounded translation invariant operators on commutative hypergroups. METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY. 2019;25(3):236–47.
- IEEE
- [1]V. Kumar, K. N. Shravan, and S. Ritumoni, “Unbounded translation invariant operators on commutative hypergroups,” METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY, vol. 25, no. 3, pp. 236–247, 2019.
@article{8669082, abstract = {{Let K be a commutative hypergroup. In this article, we study the unbounded translation invariant operators on L-p(K), 1 <= p <= infinity. For p is an element of {1, 2}, we characterize translation invariant operators on L-p(K) in terms of the Fourier transform. We prove an interpolation theorem for translation invariant operators on L-p(K) and we also discuss the uniqueness of the closed extension of such an operator on L-p(K). Finally, for p is an element of {1, 2}, we prove that the space of all closed translation invariant operators on L-p(K) forms a commutative algebra over the field of complex numbers. We also prove Wendel's theorem for densely defined closed linear operators on L-1(K).}}, author = {{Kumar, Vishvesh and N. Shravan, Kumar and Ritumoni, Sarma}}, issn = {{1029-3531}}, journal = {{METHODS OF FUNCTIONAL ANALYSIS AND TOPOLOGY}}, keywords = {{Unbounded multipliers,translation invariant operators,unbounded opera- tors,hypergroups,Fourier transform,MULTIPLIERS,SPACES}}, language = {{eng}}, number = {{3}}, pages = {{236--247}}, title = {{Unbounded translation invariant operators on commutative hypergroups}}, volume = {{25}}, year = {{2019}}, }