Related papers: Factorization theorem for the transfer function of…
We study the transfer operators for a family $F_r:[0,1] \to [0,1]$ depending on the parameter $r\in [0,1]$, which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a…
We elaborate on the consequences of the factorization of the transfer matrix of any lossless multilayer in terms of three basic matrices of simple interpretation. By considering the bilinear transformation that this transfer matrix induces…
We consider deformations of unbounded operators by using the novel construction tool of warped convolutions. By using the Kato-Rellich theorem we show that unbounded self-adjoint deformed operators are self-adjoint if they satisfy a certain…
We explore commutativity up to a factor, $AB=\lambda BA$, for bounded operators in a complex Hilbert space. Conditions on the possible values of the factor $\lambda$ are formulated and shown to depend on spectral properties of the operators…
In this paper we introduce a new family of operator-valued distributions on Euclidian space acting by convolution on differential forms. It provides a natural generalization of the important Riesz distributions acting on functions, where…
We derive the recurrence relation of irreducible tensor operator for O(4) in using the Wigner-Eckart theorem. The physical process like radiative transitions in atomic physics, nuclear transitions between excited nuclear states can be…
A general representation formula for the scattering matrix of a scattering system consisting of two self-adjoint operators in terms of an abstract operator valued Titchmarsh-Weyl $m$-function is proved. This result is applied to scattering…
Most particles in nature are unstable, manifesting as resonances in scattering processes. Using analyticity and unitarity, we show nonperturbatively that resonances, defined as poles on higher Riemann sheets of scattering amplitudes, share…
A theorem is derived which (i) provides a new class of subfactors which may be interpreted as generalized asymptotic subfactors, and which (ii) ensures the existence of two-dimensional local quantum field theories associated with certain…
We show in a unified manner that the factorization method describes completely the $L^2$-eigenspaces associated to the discrete part of the spectrum of the twisted Laplacian on constant curvature Riemann surfaces. Subclasses of two variable…
The paper provides a coherent presentation of an operator scheme, which is used in an approach to inverse problems of mathematical physics (the boundary control method). The scheme is based on the triangular factorization of operators. It…
We state several equivalent noncommutative versions of the Cauchy-Riemann equations and characterize the unbounded operators on L^2(R) which satisfy them. These operators arise from the creation operator via a functional calculus involving…
We analyze the process of two-particle scattering with unstable particle in an intermediate state. It was shown that the cross-section can be represented in the universal factorized form for an arbitrary set of particles. Phenomenological…
The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…
This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…
A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow…
Links of factorization theory, supersymmetry and Darboux transformations as isospectral deformations are considered in the context of quantum theory. The infinite chain equations for factorizing operators for a spectral problem are derived.…
Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following:…
The area related to M. Liv\v{s}ic's characteristic matrix functions is too vast to be discussed in one paper and we selected for this article the problems which are close to our scientific interests. We discuss M.Liv\v{s}ic's results…
Neat stuff about eigenfunctions, transfer matrices, and a.c. spectrum of one-dimensional Schrodinger operators