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6 papers
A theorem of Strichartz for multipliers on homogeneous trees
Sumit Kumar Rano, Rudra P. Sarkar
A theorem of Strichartz states that if a uniformly bounded bi-infinite sequence of functions on the Euclidean spaces, satisfies the condition that the Laplacian acting on a functio…
Eigenfunctions of the Laplacian satisfying Hardy-type estimates on homogeneous trees
Sumit Kumar Rano
This work deals with the characterization of eigenfunctions of the Laplacian on a homogeneous tree , which satisfy certain growth conditions. More precis…
-boundedness of pseudo-differential operators on homogeneous trees
Tapendu Rana, Sumit Kumar Rano
The aim of this article is to study the -boundedness of pseudo-differential operators on a homogeneous tree . For , we establish a connection bet…
Dynamics of semigroups generated by analytic functions of the Laplacian on Homogeneous Trees
Pratyoosh Kumar, Sumit Kumar Rano
Let be a non-constant complex-valued analytic function defined on a connected, open set containing the -spectrum of the Laplacian on a homogeneous tree. In th…
A Theorem of Roe and Strichartz on homogeneous trees
Pratyoosh Kumar, Sumit Kumar Rano
In 1980, J. Roe proved that if is doubly infinite sequence of functions in which is uniformly bounded and satisfies …
Analysis of -type estimates of Poisson transform on Homogeneous Trees
Pratyoosh Kumar, Sumit Kumar Rano
In this article we prove the restriction theorem for Helgason-Fourier transform on homogeneous tree. Our proof is based on the duality argument and the norm estimates of Poisson tr…