Related papers: Canonical systems and de Branges spaces
Extended $U_e(1)\times U_g(1)$ electromagnetism containing both a photon and a pseudo-photon is introduced at variational level and is justified by the violation of the Bianchi identities in conceptual systems, either in the presence of…
A general overview of the existing difference ring theory for symbolic summation is given. Special emphasis is put on the user interface: the translation and back translation of the corresponding representations within the term algebra and…
We apply the approach developed in our previous papers to obtain examples of solutions to the inverse spectral problem (ISP) for the canonical Hamiltonian system. One of our goals is to illustrate connections of ISP with classical tools of…
We study the indivisible intervals and the monotonicity of the growth of the exponential type in the chains of de Branges subspaces in terms of the spectral measure. We prove that for spectral measures supported on $\mathbb Z$, there exist…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
We prove that any incomplete system of complex exponentials $\{e^{i\lambda_n t}\}$ in $L^2(-\pi,\pi)$ is a subset of some complete and minimal system of exponentials. In addition, we prove analogous statement for systems of reproducing…
In the paper is we generalize known descriptions of rings of semi-invariants for regular modules over Euclidean and canonical algebras to arbitrary concealed-canonical algebras.
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
We review the Calogero-Fran\c{c}oise integrable system, which is a generalization of the Camassa-Holm system. We express solutions as (twisted) Higgs bundles, in the sense of Hitchin, over the projective line. We use this point of view to…
Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure is also exist…
We survey recent results concerning the hereditary completeness of some special systems of functions and the spectral synthesis problem for a related class of linear operators. We present a solution of the spectral synthesis problem for…
We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\mathbb{C} ^d$. Here, the full Fock space is identified…
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…
We define the notion of the canonical module of a complex. We then consider Serre's conditions for a complex and study their relationship to the local cohomology of the canonical module and its ring of endomorphisms.
The aim of this paper is to prove the existence of inductive and inverse limits of direct and inverse systems in a certain category of compact metric spaces as well as of compact metric groups. Some applications are presented.
We introduce the notion of a combinatorial inverse system in non-commutative variables. We present two important examples, some conjectures and results. These conjectures and results were suggested and supported by computer investigations.
Based on a recent paper by Rothe and Sch\"afer on compact binary systems, explicit expressions for canonical center and relative coordinates in terms of standard canonical coordinates are derived for spinless objects up to second…
Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of…
The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szeg\H{o}-type theorems for…