相关论文: Vector Continued Fractions using a Generalised Inv…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
We first survey the current state of the art concerning the dynamical properties of multidimensional continued fraction algorithms defined dynamically as piecewise fractional maps and compare them with algorithms based on lattice reduction.…
Using ordinary and exponential generating functions, we explore the reversion of power series defined by $2$nd order recurrences. We express the reversions in terms of Jacobi and Thron continued fractions. We find relations with Eulerian…
The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These…
We look for spectral type differential equations satisfied by the generalized Jacobi polynomials which are orthogonal on the interval [-1,1] with respect to a weight function consisting of the classical Jacobi weight function together with…
A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In…
The spectral decomposition for an explicit second-order differential operator $T$ is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with…
Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.
Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of $p$--adic continued fractions, i.e. continued…
We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
We describe a type of n-point function associated to strongly regular vertex operator algebras V and their irreducible modules. Transformation laws with respect to the Jacobi group are developed for 1-point functions. For certain elements…
In this article we present ways to evaluate certain sums, products and continued fractions using tools from the theory of elliptic functions. The specific results appear to be new, although similar ones can be found in the leterature; in…
We show that certain Riordan arrays have generating functions that can be expressed as continued fractions of Jacobi and Thron type. We investigate the inverses of such arrays, which in certain circumstances can also have generating…
Multi-wave inverse problems are indirect imaging methods using the interaction of two different imaging modalities. One brings spatial accuracy, and the other contrast sensitivity. The inversion method typically involve two steps. The first…
Using the six parameters truncated Mittag-Leffler function, we introduce a convenient truncated function to define the so-called truncated $\mathcal{V}$-fractional derivative type. After a discussion involving some properties associated…
Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.
The Jacobian conjecture involves the map $y= x - V(x)$ where $y, x$ are n-dimensional vectors, $V(x)$ is a symmetric polynomial of degree $d$ for which the Jacobian hypothesis holds: $ e^{Tr \ln(1- V'(x))} =1,\ \forall x$. The conjecture…
We present a method for calculating the results of operation of differential operators operating on components of vector in generalized coordinates not restricted to orthogonal one. For this we use the relationships between covariant,…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.