Abstract
We suggest a certain variant of symbolic calculus for special classes of linear bounded operators acting in Banach spaces. According to the calculus we formulate an index theorem and give applications to elliptic pseudo-differential operators on smooth manifolds with non-smooth boundaries.
Highlights
In this paper, we consider some abstract operators acting in some functional spaces.These considerations were inspired by studies of I.B
There are a lot of books in mathematics devoted to the theory of pseudo-differential operators and equations on non-smooth manifolds and manifolds with non-smooth boundaries [5,6,7,8,9,10], but it seems that the suggested abstract variant is very close to this theory
To obtain invertibility conditions for local operators, we need some additional characteristics for the classical symbol of elliptic pseudo-differential operators
Summary
We consider some abstract operators acting in some functional spaces These considerations were inspired by studies of I.B. Simonenko [1] related to special operators of a local type (we say here local operators). Some first steps were done in the author’s paper [11], and here we develop this abstract variant and give some applications We think this approach can be useful for similar problems related to concrete operators. This way for elliptic pseudo-differential equations was suggested by the author earlier and partially described in his works of that period: at least two-dimensional situation was desxribed exactly (such results and review can be found in [4]). We deal with a multi-dimensional version of the Wiener–Hopf method [12] or one of analogues of the Riemann boundary value problem [13,14]
Sign-in/Register to view highlights & summary 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.
