Abstract In the setting of higher-dimensional anisotropic Heisenberg group, we compute fundamental solution for sub-Laplacian, and prove Poincaré $$\beta $$ ? -Logarithmic Sobolev inequalities measures as a function this solution.

A bstract We investigate 2 n -dimensional axion electrodynamics for the purpose of exploring a higher-group structure underlying it. This is manifested as Green-Schwarz transformation background gauge fields that couple minimally to conserved currents. The = 3 case studied most intensively. derive identities correlation functions among global symmetry generators by using maps two with each othe...

Shearlets emerged in recent years in applied harmonic analysis as a general framework to provide sparse representations of multidimensional data. This construction was motivated by the need to provide more efficient algorithms for data analysis and processing, overcoming the limitations of traditional multiscale methods. Particularly, shearlets have proved to be very effective in handling direc...

in this paper, we focus on the study of shearlet transform which isde ned by using the hyperbolic functions. as a result we check an admissibilitycondition such that implies the reconstruction formula. to this end, we will usethe concept of the classical shearlet, which indicates the position and directionof a singularity.

3 Computation of the shearlet transform 13 3.1 Finite discrete shearlets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.2 A discrete shearlet frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 Inversion of the shearlet transform . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.4 Smooth shearlets . . . . . . . . . . . . . . . . . . . . . . . . . ...