Related papers: The Wavelet Galerkin Operator
Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the…
For an arbitrary generalized quantum integrable spin chain we introduce a "master T -operator" which represents a generating function for commuting quantum transfer matrices constructed by means of the fusion procedure in the auxiliary…
We demonstrate in the context of the minisuperspace model consisting of a closed Friedmann-Robertson-Walker universe coupled to a scalar field that Vilenkin's tunneling wavefunction can only be consistently defined for particular choices of…
The original intent of the Koopman-von Neumann formalism was to put classical and quantum mechanics on the same footing by introducing an operator formalism into classical mechanics. Here we pursue their path the opposite way and examine…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
A waveguide G lies in the (n+1)-dimensional Euclidean space for positive integer n, and outside a large ball coincides with the union of finitely many non-overlapping semi-cylinders ("cylindrical ends"). The waveguide is described by the…
The present article is devoted to the generalized Salem functions, the generailed shift operator, and certain related problems. A description of further investigations of the author of this article is given.These investigations (in terms of…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point…
We study relations between non-commutative Ruelle transfer operators over the C$^*$-algebra $B(\mathcal{H})$ of linear bounded operators over separable Hilbert spaces $\mathcal{H}$ (infinite-dimensional) and other completely positive maps.…
We revise a monogenic calculus for several non-commuting operators, which is defined through group representations. Instead of an algebraic homomorphism we use group covariance. The related notion of joint spectrum and spectral mapping…
Commuting integral and differential operators connect the topics of Signal Processing, Random Matrix Theory, and Integrable Systems. Previously, the construction of such pairs was based on direct calculation and concerned concrete special…
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…
In this paper, we construct a Q-operator as a trace of a representation of the universal R-matrix of $U_q(\hat{sl}_2)$ over an infinite-dimensional auxiliary space. This auxiliary space is a four-parameter generalization of the q-oscillator…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…
We provide explicit commutative sequence space representations for classical function and distribution spaces on the real half-line. This is done by evaluating at the Fourier transforms of the elements of an orthonormal wavelet basis.
The transfer property for the generalized Browder's theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$-Weyl spectrum inclusion. In addition, the isolated points of…
We give an operator theoretic approach to the constructions of multiresolutions as they are used in a number of basis constructions with wavelets, and in Hilbert spaces on fractals. Our approach starts with the following version of the…
This research article discusses a numerical solution of the radiative transfer equation based on the weak Galerkin finite element method. We discretize the angular variable by means of the discrete-ordinate method. Then the resulting…