arXiv subjects

Elmar Pauwels

Publications and source records attributed to Elmar Pauwels.

2 recordsLinked to original sources

arXiv2014

On the prolate spheroidal wave functions and Hardy's uncertainty principle

We prove a weak version of Hardy's uncertainty principle using properties of the prolate spheroidal wave functions (PSWFs). We describe the eigenvalues of the sum of a time limiting operator and a band limiting operator acting on L2(R). A weak version of Hardy's uncertainty principle follows from the asymptotic behavior of the largest eigenvalue as the time limit and the band limit approach infinity. An asymptotic formula for this eigenvalue is obtained from its well-known counterpart for the prolate integral operator.

math.FA↗

arXiv2012

Uniqueness and Reconstruction Theorems for Pseudodifferential Operators with a Bandlimited Kohn-Nirenberg Symbol

Motivated by the problem of channel estimation in wireless communications, we derive a reconstruction formula for pseudodifferential operators with a bandlimited symbol. This reconstruction formula uses the diagonal entries of the matrix of the pseudodifferential operator with respect to a Gabor system. In addition, we prove several other uniqueness theorems that shed light on the relation between a pseudodifferential operators and its matrix with respect to a Gabor system.

math.FA↗