Dr. Sneh Lata, Assistant Professor, Department of Mathematics, has received a 3 year research grant of 2 Lakhs per annum from Science and Engineering Research Board (SERB), DST, Gov. of India under the scheme Mathematical Research Impact Centric Support (MATRICS). The title of the project is “Investigating a Class of Operators on Certain Hilbert Spaces and Their Connection to Frame Theory”. She describes the setting of her recent work as follows:
"There is a well-known result of de Branges that characterizes all Hilbert spaces which are contractively contained in the Hardy space H2 and on which the operator of multiplication with the coordinate function z acts isometrically. This result is a generalization of the famous invariant subspace theorem of Beurling, and is the starting point of a model theory for operators initiated by de Branges and Rovanyak. Very recently, we have been able to generalize this result of Beurling. In one of my earlier work, we characterize a class of sub-Lebesgue Hilbert spaces which are closely related to the work of de Branges. This work seems to have some connections with frame theory."
In this project, Sneh plans to investigate the above named Hilbert spaces and some other Hilbert spaces from operator-theoretic view point such as via decomposition or through their invariant subspaces and explore, if possible, their connections with frame theory.
Sneh is also currently serving as the department's graduate advisor.