Related papers: Transfer operators and Hankel transforms: horosphe…
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…
The review of star-product formalism providing the possibility to describe quantum states and quantum observables by means of the functions called symbols of operators which are obtained by means of bijective maps of the operators acting in…
In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite Fuchsian groups to the Hecke triangle groups G_q, q=3,4,..., which are non-arithmetic for q \not= 3,4,6. For this we make use of a Poincare map…
We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's…
We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
For fixed real numbers $c>0,$ $\alpha>-\frac{1}{2},$ the finite Hankel transform operator, denoted by $\mathcal{H}_c^{\alpha}$ is given by the integral operator defined on $L^2(0,1)$ with kernel $K_{\alpha}(x,y)= \sqrt{c xy}…
We use the method of atomic decomposition and a new family of Banach spaces to study the action of transfer operators associated to piecewise-defined maps. It turns out that these transfer operators are quasi-compact even when the…
We describe rigorous quantum measurement theory in the Heisenberg picture by applying operator deformation techniques previously used in noncommutative quantum field theory. This enables the conventional observables (represented by…
We discuss generalizations of the Langlands program, from reductive groups to the local and automorphic spectra of spherical varieties, and to more general representations arising as "quantizations" of suitable Hamiltonian spaces. To a…
A non-commuting measurement transfers, via the apparatus, information encoded in a system's state to the external "observer". Classical measurements determine properties of physical objects. In the quantum realm, the very same notion…
This paper provides the connection between the Hankel transform and aerating transforms of a given integer sequence. Results obtained are used to establish a completely different Hankel transform evaluation of the series reversion of a…
In this paper we present uniform weighted inequalities for the Hankel transform transplantation operator. A weighted vector-valued inequality is also obtained. As a consequence we deduce an extension of a transference theorem due to Rubio…
To a pair of subspaces wandering with respect to a row isometry we associate a transfer function which in general is multi-Toeplitz and in interesting special cases is multi-analytic. Then we describe in an expository way how characteristic…
A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…
The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the…
We explicitly determine the spectrum of transfer operators (acting on spaces of holomorphic functions) associated to analytic expanding circle maps arising from finite Blaschke products. This is achieved by deriving a convenient natural…
We discuss an application of the transfer operator approach to the analysis of the different spectral characteristics of 1d random band matrices (correlation functions of characteristic polynomials, density of states, spectral correlation…
We use tools from non-standard analysis to formulate the building blocks of quantum field theory within the framework of categorical quantum mechanics. Building upon previous work, we construct an object of *Hilb having quantum fields as…
Let $G$ be a locally compact abelian group with a Haar measure, and $Y$ be a measure space. Suppose that $H$ is a reproducing kernel Hilbert space of functions on $G\times Y$, such that $H$ is naturally embedded into $L^2(G\times Y)$ and is…