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Unbounded translation invariant operators on commutative hypergroups

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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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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}},
}