Related papers: Remling's Theorem on canonical systems
We prove a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces.
The Nevanlinna matrix of a half-line Jacobi operator coincides, up to multiplication with a constant matrix, with the monodromy matrix of an associated canonical system. This canonical system is discrete in a certain sense, and is…
We develop Jacobson's refinement of Engel's Theorem for Leibniz algebras. We then note some consequences of the result.
We develop Hamilton-Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a…
We present the first representation of the general term of the Rayleigh-Schr\"odinger series for quasidegenerate systems. Each term of the series is represented by a tree and there is a straightforward relation between the tree and the…
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
A simple and illustrative rheonomic system is explored in the Lagrangian formalism. The difference between Jacobi's integral and energy is highlighted. A sharp contrast with remarks found in the literature is pointed out. The…
We obtain some results related to Romanoff's theorem.
This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective…
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
We prove the abundance theorem for numerically trivial log canonical divisors of log canonical pairs and semi-log canonical pairs.
An alternative proof of the duality of generalized Lie bialgebroid is given and proved a canonical Jacobi structure can be defined on the base of it. We also introduce the notion of morphism between generalized Lie bialgebroids and proved…
The present study provides another look on Lamperti's theorem on recurrence or transience of stochastic sequences. We establish connection between Lamperti's theorem and the recent result by the author [V. M. Abramov, Theor. Probab. Math.…
On the basis of the first principle -- the law of probability conservation and the Helmholtz decomposition theorem the authors have succeeded to construct the Schr\"odinger, Pauli, Dirac equation, the Hamilton-Jacobi equation and the…
We establish a new equivalent condition for the Grand Riemann Hypothesis for L-functions in a wide subclass of the Selberg class in terms of canonical systems of differential equations. A canonical system is determined by a real symmetric…
We formulate and prove an analogue of Beurling's theorem for the Fourier transform on the Heisenberg group. As a consequence we deduce Hardy and Cowling-Price theorems.
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
The evolution equation for the propagator of the quantum system in the optical probability representation (optical propagator) is obtained. The relations between the optical and quantum propagators for the Schr\"odinger equation and the…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
It is proved that feedback classification of a linear system over a commutative von Neumann regular ring R can be reduced to the classification of a finite family of systems, each of which is properly split into a reachable and a…