Use of Frames in Sampling Theory

Antonio García García was born in Valladolid, Spain, in 1957. He received M.Sc. degree in mathematics in 1979 and a Ph.D. in mathematics in 1983, both from the University of Valladolid, Spain. After teaching mathematics in a high school, he joined, in 1991, the Department of Mathematics of the University Carlos III de Madrid, Spain, as an Associate Professor. Since 2009, he has held a full professor position. His research interests include all the mathematical topics related to sampling theory, where he has 6 Ph.D. students, and he has published 71 papers in periodic journals and 5 book chapters (4 in Springer books). H has also written 2 textbooks (in Spanish). He was the main researcher of 5 research projects on the sampling topic. More information can be found on his personal webpage.

• - What does sampling theory mean?.- Basic sampling theory.- Sampling in shift-invariant subspaces.- A review on Kramer sampling theorem.- A generalized sampling theory.- Finite frames related to sampling in finite-dimensional U-invariant subspaces.- Sampling in shift-invariant-like subspaces of Hilbert-Schmidt operators.