Alladi Ramakrishnan Hall

Sampling Theory in Shift-invariant Spaces

Anthony Selvan

IMSc

In this talk, we  discuss Shannon-type sampling formulas,
Kadec-type theorems, and Beurling-Landau-type theorems for shift-invariant
spaces. We  provide  the sharp maximum gap condition for a  sampling set in
the shift-invariant space generated by Meyer scaling functions. This is an
open problem (sampling density condition for shift invariant spaces)
 proposed by  Aldroubi and Grochenig in 2000.  Finally, we discuss a new
sampling density condition for shift-invariant spaces.