Related papers: Residues and Telescopers for Rational Functions
We apply a recently developed semiclassical theory of short periodic orbits to the continuously open quantum tribaker map. In this paradigmatic system the trajectories are partially bounced back according to continuous reflectivity…
We classify those rational maps $f: \mathbb{P}^1 \to \mathbb{P}^1$ for which there exists a contravariant tensor $q$ which is parallel, i.e. such that $f^*q // q$, by proving that such maps preserve a parabolic orbifold.
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…
The objective of this paper is to improve the customary definition of redundancy by providing quantitative measures in its place, which we coin upper and lower redundancies, that match better with an intuitive understanding of redundancy…
A class of spherical functions is studied which can be viewed as the matrix generalization of Bessel functions. We derive a recursive structure for these functions. We show that they are only special cases of more general radial functions…
Rational maps on the Riemann sphere occupy a distinguished niche in the general theory of smooth dynamical systems. First, rational maps are complex-analytic, so a broad spectrum of techniques can contribute to their study (quasiconformal…
Using the complete orthonormal basis sets of nonrelativistic and quasirelativistic orbitals introduced by the author in previous papers for particles with arbitrary spin the new analytical relations for the -component relativistic tensor…
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
We argue about the following concepts:(i)introduction of endo and exo-observer of a physical system (ii) possible relation between endo, exo-observer and continuum/discrete nature of the same system (iii)the distinction about two categories…
Rational observers are to be constructed for rational systems while polynomial observers are to be constructed for polynomial systems. An observer synthesis procedure is formulated. First an output-based rational realization is synthesized…
We attempt to dissolve the measurement problem using an anthropic principle which allows us to invoke rational observers. We argue that the key feature of such observers is that they are rational (we need not care whether they are…
This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We…
A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1]…
This paper is a continuation of our study of a class of Toeplitz-like operators with a rational symbol which has a pole on the unit circle. A description of the spectrum and its various parts, i.e., point, residual and continuous spectrum,…
In the second part of our work on observables we have shown that quantum observables in the sense of von Neumann, i.e.bounded selfadjoint operators in some von Neumann subalgebra $R$ of $L(H)$, can be represented as bounded continuous…
In this second article of the series we study holomorphic families of generic rational matrix functions parameterized by the pole and zero loci. In particular, the isoprincipal deformations of generic rational matrix functions are proved to…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
We describe a general method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of…
For arbitrary linear time-invariant systems, the existence of a strong functional observer is investigated. Such observer determines, from the available measurement on the plant, an estimate of a function of the state and the input. This…