**Speaker:**Rakesh Balhara

**Date:**4th September 2018

**Time:**9:15pm-10:15pm

**Venue:**Lecture Hall 1, Department of Mathematics

**Abstract:**

We will consider an extension problem and relate its solution to the fractional powers of the Grushin operator. The same stuff has been done for Laplacian on R^n, so we will start with Laplacian case in order to understand this technique of defining fractional power of an operator via extension problem. Further we will derive trace-Hardy inequality and subsequently Hardy’s inequality for the fractional power of Grushin operator using the extension problem technique.

**Prerequisites:**Basic Functional Analysis

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