Discrete Laplacian Operator and Its Applications in Signal Processing

Preclosure operator and its applications in general topology

In this paper, we show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

Discrete Time Signal Processing

Discrete Signal Processing Notes

Signal Representation and Processing Using Operator Groups

This thesis presents a signal representation in terms of operators The signal is as sumed to be an element of a vector space and subject to transformations of operators The operators form continuous groups so called Lie groups The representation can be used for signals in general in particular if spatial relations are unde ned and it does not require a basis of the signal space to be useful Spe...

Convexity of the first eigenfunction of the drifting Laplacian operator and its applications

In this short note, we prove the convexity of the first eigenfunction of the drifting Laplacian operator with zero Dirichlet boundary value provided a suitable assumption to the drifting term is added. After giving a gradient estimate, we then use the convexity of the first eigenfunction to get a lower bound of the difference of the first and second eigenvalues of the drifting Laplacian.