相关论文: Eigenfunctions of transfer operators and cohomolog…
For the group PSL(2,Z) it is known that there is an isomorphism between polynomial eigenfunctions of the transfer operator for the geodesic flow and the Eichler cohomology in the theory of modular forms. In a recent paper by Chang and Mayer…
We study the spectral properties of a family of generalized transfer operators associated to the Farey map. We show that when acting on a suitable space of holomorphic functions, the operators are self-adjoint and the positive dominant…
In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…
In this article we report on a surprising relation between the transfer operators for the congruence subgroups $\Gamma_{0}(n)$ and the Hecke operators on the space of period functions for the modular group $\PSL (2,\mathbb{Z})$. For this we…
We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms,…
Let L be the transfer operator associated with the Gauss' continued fraction map, known also as the Gauss-Kuzmin-Wirsing operator, acting on the Banach space. In this work we prove an asymptotic formula for the eigenvalues of L. This…
Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding eigenfunctions of transfer operators based on comparing Gibbs…
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional analysis behind the transfer operators for triangle…
The time periodic circuit theory is exploited to introduce an appropriate translation operator that is invariant under the change of the spatial unit cell. Useful properties of the operator are derived. By casting the problem in an…
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…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators
Transfer operators such as the Perron--Frobenius or Koopman operator play an important role in the global analysis of complex dynamical systems. The eigenfunctions of these operators can be used to detect metastable sets, to project the…
We consider self-similar measures on $\mathbb R.$ The Hutchinson operator $H$ acts on measures and is the dual of the transfer operator $T$ which acts on continuous functions. We determine polynomial eigenfunctions of $T .$ As a…
In this paper we point out an connection between eigenfunctions of one-dimensional Schrodinger operator with polynomial potentials of degree 3, 4 and eigenfunctions of rank two commuting ordinary differential operators.
We establish an eigenfunctional theorem for positive operators, evocative of the Krein--Rutman theorem. A more general version gives a joint eigenfunctional for commuting operators.
We consider transfer operators acting on spaces of holomorphic functions, and provide explicit bounds for their eigenvalues. More precisely, if D is any open set in C^d, and L is a suitable transfer operator acting on Bergman space A^2(D),…
We consider the problem of showing that 1 is an eigenvalue for a family of generalised transfer operators of the Farey map. This problem is related to the spectral theory of the modular surface via the Selberg Zeta function and the theory…
The localization phenomenon for periodic unitary transition operators on a Hilbert space consisting of square summable functions on an integer lattice with values in a complex vector space, which is a generalization of the discrete-time…
The spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analytic functions they are self-adjoint and exhibit absolutely…
We prove rapid decay (even exponential decay under some stronger assumptions) of the eigenfunctions associated to discrete eigenvalues, for a class of self-adjoint operators in $L^2(\mathbb{R}^d)$ defined by ``magnetic'' pseudodifferential…