Related papers: On infinite-dimensional limit of the Steinberg rep…
Contrary to the finite-dimensional case, the Moebius group admits interesting self-representations when infinite-dimensional. We construct and classify all these self-representations. The proofs are obtained in the equivalent setting of…
It is well known that linear and non-linear dissipative port-Hamiltonian systems in finite dimensions admit an energy balance, relating the energy increase in the system with the supplied energy and the dissipated energy. The integrand in…
We give an unique string representation, up to isomorphism, for initially connected deterministic finite automata (ICDFAs) with n states over an alphabet of k symbols. We show how to generate all these strings for each n and k, and how its…
The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are…
The problem of representation of elements of weighted space of infinitely differentiable functions on real line by exponential series is considered.
The aim of this paper is to extend the structure theory for infinitely generated modules over tame hereditary algebras to the more general case of modules over concealed canonical algebras. Using tilting, we may assume that we deal with…
In this paper a free analogous of completely random measure is introduced. Furthermore, a representation theorem is proved for free completely random measures that are free infinitely divisible.
We present a unified approach to quantum teleportation in arbitrary dimensions based on the Wigner-function formalism. This approach provides us with a clear picture of all manipulations performed in the teleportation protocol. In addition…
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous…
It is shown that certain natural quantum logic gates, {\it i.e.} unitary time evolution matrices for spin-\frac{1}{2} quantum spins, can be represented as sums, with appropriate phases, over classical logic gates, in a direct analogy with…
We present a modification of Riesz's construction of the Lebesgue integral, leading directly to finite or infinite integrals, at the same time simplifying the proofs.
We show that two-dimensional billiard systems are Turing complete, in the sense that the halting of any Turing machine with a given input is equivalent to a certain bounded trajectory in this system entering a specified open set. Billiards…
We investigate the problem of balanced embedding of a non-compact complex manifold into an infinite-dimensional projective space. In this paper we prove the existence of such an embedding in a model case. The strategy is by using a gradient…
We propose a notion of autoreducibility for infinite time computability and explore it and its connection with a notion of randomness for infinite time machines.
We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…
A realization of a deformed Lorentz algebra is considered and its irreducible representations are found; in the limit $q\to 1$, these are precisely the irreducible representations of the classical Lorentz group.
In this paper we apply the instanton representation method to the construction of spherically symmetric blackhole general relativity solutions. The instanton representation implies the existence of additional Type D solutions which are…
The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution…
We describe the exponential map from an infinite-dimensional Lie algebra to an infinite-dimensional group of operators on a Hilbert space. Notions of differential geometry are introduced for these groups. In particular, the Ricci curvature,…
We introduce a simple deformed quantization prescription that interpolates the classical and quantum sectors of Weinberg's nonlinear quantum theory. The result is a novel classical limit where $\hbar$ is kept fixed while a dimensionless…