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A primer on eigenvalue problems of non-self-adjoint operators
Non-self adjoint operators describe problems in science and engineering that lack symmetry and unitarity. They have applications in...
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Product Approximations of Self-Adjoint Semigroups
In this chapter, we proceed with a systematic analysis of the main for this book subject: the product formulæ approximations in the operator-norm...
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Transmutations for Self-Adjoint Differential Operators
AbstractMade equations for the kernel of the transformation operator in self-adjoin differential operators. The main factor that makes it possible to...
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On creating new essential spectrum by self-adjoint extension of gapped operators
Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily...
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Generic Stability for Self-Adjoint Semigroups
Category theorems for self-adjoint semigroups are presented; for some classes of self-adjoint semigroups, it is shown that, typically in Baire’s...
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Models of Self-Adjoint and Unitary Operators in Pontryagin Spaces
This article is a revised version of the lectures given by the author at KROMSH-2019. These lectures are devoted to describing a few different ways...
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Classical Self-Adjoint Extension Schemes
This chapter presents the two classical self-adjoint extension theories a la von Neumann and a la Kreı̆n, Višik, and Birman. We start with the...
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Self-adjoint Operators and Spectra
In this chapter, we summarize basic knowledge from functional analysis for the spectral theory needed in later arguments. Starting from the...
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Recent Developments in Spectral Theory for Non-self-adjoint Hamiltonians
The objective of this survey is to collect and elaborate on different tools, both well-established and more recent ones, which have been developed in...
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The Positive and Negative Deficiency Indices of Formally Self-Adjoint Difference Equations
This paper is concerned with formally self-adjoint difference equations and their positive and negative deficiency indices. It is shown that the...
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Distance Between Unitary Orbits of Self-Adjoint Elements in C*-Algebras of Tracial Rank One
The note studies certain distance between unitary orbits. A result about Riesz interpolation property is proved in the first place. Weyl (1912) shows...
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Self-Adjoint Extension Schemes and Modern Applications to Quantum Hamiltonians
This book introduces and discusses the self-adjoint extension problem for symmetric operators on Hilbert space. It presents the classical von Neumann...
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Characterizations of Ordered Self-adjoint Operator Spaces
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as
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On a General Approach to Construction of a Self-Adjoint Dilation for a Dissipative Operator
We propose a general approach to the construction of a self-adjoint dilation for a densely defined dissipative operator with a non-empty set of...
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Electromagnetic Steklov eigenvalues: existence and distribution in the self-adjoint case
In previous works, it was suggested to use Steklov eigenvalues for Maxwell equations as target signature for nondestructive testing, and it was...
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Generalities on Symmetric and Self-Adjoint Operators on Hilbert Space
This chapter of preliminaries collects all the necessary theoretical pre-requisites from Hilbert space operator theory, and self-adjoint operator...