Speaker: Dr. Shivam Bajpeyi, IIT Delhi Date and Time: 14 April 1400-1445 Online seminar link: meet.google.com/twc-rhog-bkf
Classical and Random Sampling in Different Function Spaces
In 1949, Shannon pioneered the idea of reconstructing band-limited signals with the help of equally spaced sample values of the signal. Later, Butzer et.al. established that the approximation of not- necessarily band-limited signals is possible via infinite sampling series. In this talk, I will discuss the approximation properties of a family of sampling operators that approximate a certain class of functions in case the available sampling data is not equally spaced, but exponentially spaced.
Further, I will talk about the problem of random sampling where the sample positions are selected randomly rather than in a fixed pattern, and we estimate the probability of the stable recovery of any given signal in a function space. We will examine the random sampling problem for a class of Mellin band-limited signals, and also in reproducing kernel subspace of Orlicz space.