Matrix representations of multidimensional integral and ergodic operators
Abstract
We provide a representation of the $C^*$algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the explicit functional calculus on this algebra. The method can be useful in various applications since many discrete approximations of integral and differential operators belong to this algebra. Some examples are also presented: 1) we construct an explicit functional calculus for extended Fredholm integral operators with piecewise constant kernels, 2) we find a wave function and spectral estimates for 3D discrete Schrödinger equation with planar, guided, local potential defects, and point sources. The accuracy of approximation of continuous multikernel integral operators by the operators with piecewise constant kernels is also discussed.
 Publication:

arXiv eprints
 Pub Date:
 May 2018
 arXiv:
 arXiv:1805.09100
 Bibcode:
 2018arXiv180509100K
 Keywords:

 Mathematical Physics
 EPrint:
 few misprints are corrected, e.g. before (68) indices ij