Related papers: Canonical systems and de Branges spaces
Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces. One application characterizes the existence of a kind of generalized universal cover.
We utilize the theory of de Branges spaces to show when certain Schr\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness…
We solve direct and inverse problems for two-dimensional (quasi) canonical systems related to exponential polynomials of a specific but sufficiently general type. The approach to the inverse problem in this paper provides an interpretation…
The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the…
Dynamical canonical systems and their connections with the classical (spectral) canonical systems are considered. We construct B\"acklund-Darboux transformation and explicit solutions of the dynamical canonical systems. We study also those…
The canonical partition function of a system of rotators (classical X-Y spins) on a lattice, coupled by terms decaying as the inverse of their distance to the power alpha, is analytically computed. It is also shown how to compute a…
We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…
This is a survey of the inverse spectral problem on (mainly compact) Riemannian manifolds, with or without boundary. The emphasis is on wave invariants: on how wave invariants have been calculated and how they have been applied to concrete…
We prove that the nearly invariant subspaces of a de Branges space which have no common zeros are precisely of the form an exponential function times a de Branges space.
In this paper we define canonical sine and cosine transform, convolution operations, prove convolution theorems in space of integrable functions on real space. Further, obtain some results require to construct the spaces of integrable…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
We characterize all bounded Hankel operators $\Gamma $ such that $\Gamma^*\Gamma$ has finite spectrum. We identify spectral data corresponding to such operators and construct inverse spectral theory including the characterization of these…
This note focuses on recent results in spectral analysis of canonical systems of differential equations obtained via the approach developed in our previous papers \cite{MIF1, MP3, etudes, etudes2, PZ, Direct}. Many of our results are…
We solve completely the spectral synthesis problem for reproducing kernels in the de Branges spaces $\mathcal{H}(E)$. Namely, we describe the de Branges spaces $\mathcal{H}(E)$ such that all $M$-bases of reproducing kernels (i.e., complete…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in…
This paper extends the concept of de Branges matrices to any finite $m\times m$ order where $m=2n$. We shall discuss these matrices along with the theory of de Branges spaces of $\mathbb{C}^n$-valued entire functions and their associated…
A string basis is constructed for each subalgebra of invariants of the function algebra on the quantum special linear group. By analyzing the string basis for a particular subalgebra of invariants, we obtain a ``canonical basis'' for every…
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
The multichannel generalization of the theory of spectral, scattering and decay control is presented. New universal algorithms of construction of complex quantum systems with given properties are suggested. Particularly, transformations of…