Modelling modal based sensors for oscillatory systems

In this paper we very briefly describe a class of sensors which have proven very useful in control problems for distributed parameter systems. These sensors, which provide approximate point evaluation for infinite dimensional systems, also rapidly damp high frequency oscillations. The sensors are obtained as convolution integrals over small spatial regions with kernels that possess rather interesting properties. In this work we very briefly describe the kernels, give some of their important properties. We expect that the underlying kernels will find many applications in other areas where there is a desire to have smooth compactly supported sensors that rapidly damp the effects of high frequency modes. In particular, these kernels can be used as efficient small-scale spatial mollifiers with efficient spectral filtering properties in computational fluid dynamics.