Abstract
In this and the following chapter, we will discuss the spectrum of a closed operator A. We know that we can form a disjoint decomposition of. The discrete spectrum of A, σd(A), consists of isolated eigenvalues of finite algebraic multiplicity, and σess(A), the essential spectrum of A, is the remaining part of the spectrum. We will study σd(A) in this chapter through the projection operators that can be obtained from the resolvent of A for each distinct eigenvalue in σd(A). We develop the basic theory of these projections, called Riesz projections. These operators provide a powerful tool for the study of the discrete spectrum of closed operators.
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.
