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 multi-kernel integral operators by the operators with piecewise constant kernels is also discussed.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
