Related papers: Spectral structure of transfer operators for expan…
It is well established that the physical phenomenon of intermittency can be investigated via the spectral analysis of a transfer operator associated with the dynamics of an interval map with indifferent fixed point. We present here for the…
Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties…
We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the…
We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…
We construct and study a functorial extension of the evaluation map $S^1 \times \mathcal{L} X \to X$ to transfers along finite covers. For finite covers of classifying spaces of finite groups, we provide algebraic formulas for this…
We analyze the singular spectrum of selfadjoint operators which arise from pasting a finite number of boundary relations with a standard interface condition. A model example for this situation is a Schroedinger operator on a star-shaped…
The resolvent function of an operator in a Banach space is defined on an open subset of the complex plane and is holomorphic. It obeys the resolvent equation. A generalization of this equation to Schwartz distributions is defined and a…
We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.
We consider the analytic continuation of the transfer function associated with a 2x2 operator matrix having unbounded couplings into unphysical sheets of its Riemann surface. We construct a family of non-selfadjoint operators which…
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix viewed as a weight matrix on a finite directed path graph…
We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted…
The main objective of this paper is to develop a notion of joint spectrum for complex solvable Lie algebras of operators acting on a Banach space, which generalizes the Taylor joint spectrum (T.J.S.) for several commuting operators.
The main purpose of this work is the construction of an analytic functional calculus for Clifford operators, which are operators acting on certain modules over Clifford algebras. Unlike in some preceding works by other authors, we use a…
Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functional analysis behind the transfer operator of each of these…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We study holomorphic extensions of one-parameter groups on locally convex spaces with a view to applications to KMS boundary conditions. In the first part we deal with analytic extensions of one-parameter groups of operators on locally…
We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main…
We develop the spectral and scattering theory for self-adjoint Hankel operators $H$ with piecewise continuous symbols. In this case every jump of the symbol gives rise to a band of the absolutely continuous spectrum of $H$. We construct…
We develop a holomorphic functional calculus for (multivalued linear) operators on locally convex vector spaces. This includes the case of fractional powers along Lipschitz curves.
A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of…