N. Sh. Kumar

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Articles: 2

Representations of the Orlicz Figà-Talamanca Herz algebras and Spectral Subspaces

Rattan Lal, N. Shravan Kumar

↓ Abstract   |   Article (.pdf)

MFAT 26 (2020), no. 2, 169-178


Let $G$ be a locally compact group. In this note, we characterise non-degenerate $*$-representations of $A_\Phi(G)$ and $B_\Phi(G).$ We also study spectral subspaces associated to a non-degenerate Banach space representation of $A_\Phi(G).$

Unbounded translation invariant operators on commutative hypergroups

Vishvesh Kumar, N. Shravan Kumar, Ritumoni Sarma

↓ Abstract   |   Article (.pdf)

MFAT 25 (2019), no. 3, 236-247


Let $K$ be a commutative hypergroup. In this article, we study the unbounded translation invariant operators on $L^p(K),\, 1\leq p \leq \infty.$ For $p \in \{1,2\},$ 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 $p \in \{1,2\},$ 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 $L^1(K).$

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