Journal of Spectral Theory

Spectral Theory

Spectral theory has for its origin the classical theory of finite matrices and, in a sense, includes all theories which may be specialized to some particular phase of that classical theory. Such a meaning for the term spectral theory is perhaps too broad, for its acceptance would force one, as is becoming increasingly evident, to admit that spectral theory embraces not a small part of such fiel...

Spectral Theory

Spectral Theory

In many applications it is important to understand the spectral properties of a linear operator T : X → X, where X is some vector space over IR or I C. In the finite dimensional (complex) case linear operators may be characterised as matrices and the Jordan normal form theorem applies, providing a basis of generalised eigenvectors. If, in addition, T is normal (i.e. T and T ∗ commute) with resp...

Spectral Theory

These are notes from two lectures given in MATH 27200, Basic Functional Analysis, at the University of Chicago in March 2010. The proof of the spectral theorem for compact operators comes from [Zim90, Chapter 3]. 1. The Spectral Theorem for Compact Operators The idea of the proof of the spectral theorem for compact self-adjoint operators on a Hilbert space is very similar to the finite-dimensio...

Spectral theory of corrugated surfaces

This paper is a brief review of the program initiated some years ago in [JMP]. The main goal of this program is to understand the formation and the propagation properties of surface states in regions with corrugated boundaries. The history of this problem and its physical aspects are discussed in [JMP, KP]. The results described in this review are obtained in collaborations with Yoram Last and ...