scholarly journals Variational characterizations for eigenfunctions of analytic self-adjoint operator functions

2013 ◽  
Vol 33 (2) ◽  
pp. 307 ◽  
Author(s):  
Georgis Katsouleas ◽  
John Maroulas
Keyword(s):  
Adjoint Operator ◽  
Operator Functions

scholarly journals COMMUTATOR ESTIMATES AND $\RR$-FLOWS IN NON-COMMUTATIVE OPERATOR SPACES

2007 ◽  
Vol 50 (2) ◽  
pp. 293-324 ◽  
Author(s):  
Ben de Pagter ◽  
Fyodor Sukochev
Keyword(s):  
Symmetric Operator ◽  
Von Neumann Algebra ◽  
Adjoint Operator ◽  
Operator Spaces ◽  
Von Neumann ◽  
Finite Von Neumann Algebra ◽  
Operator Functions ◽  
Strongly Continuous Groups ◽  
Symmetric Operator Spaces ◽  
Groups Of Isometries

AbstractThe principal results in this paper are concerned with the description of domains of infinitesimal generators of strongly continuous groups of isometries in non-commutative operator spaces $E(\mathcal{M},\tau)$, which are induced by $\mathbb{R}$-flows on $\mathcal{M}$. In particular, we are concerned with the description of operator functions which leave the domain of such generators invariant in all symmetric operator spaces, associated with a semi-finite von Neumann algebra $\mathcal{M}$ and a separable function space $E$ on $(0,\infty)$. Furthermore, we apply our results to the study of operator functions for which $[D,x]\in E(\mathcal{M},\tau)$ implies that $[D,f(x)]\in E(\mathcal{M},\tau)$, where $D$ is an unbounded self-adjoint operator. Our methods are partly based on the recently developed theory of double operator integrals in symmetric operator spaces and the theory of adjoint $C_{0}$-semigroups.

The Virozub–Matsaev Condition and Spectrum of Definite Type for Self-adjoint Operator Functions

2007 ◽  
Vol 2 (1) ◽  
pp. 99-134 ◽  
Author(s):  
Heinz Langer ◽  
Matthias Langer ◽  
Alexander Markus ◽  
Christiane Tretter
Keyword(s):  
Adjoint Operator ◽  
Operator Functions

scholarly journals Triple variational principles for self-adjoint operator functions

2016 ◽  
Vol 270 (6) ◽  
pp. 2019-2047 ◽  
Author(s):  
Matthias Langer ◽  
Michael Strauss
Keyword(s):  
Variational Principles ◽  
Adjoint Operator ◽  
Operator Functions

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Adjoint Operator ◽  
Integral Kernel ◽  
Mathematical Finance ◽  
Elliptic Operators ◽  
Complete Analysis ◽  
Time Behavior ◽  
Degenerate Elliptic Operators ◽  
Regularity Properties ◽  
Degenerate Elliptic ◽  
Mathematical Foundations

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the martingale problem and therefore the existence of the associated Markov process. The book uses an “integral kernel method” to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. The book establishes the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. It shows that the semigroups defined by these operators have holomorphic extensions to the right half plane. The book also demonstrates precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

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