Related papers: Generalised power series determined by linear recu…
An abstract theory of Fourier series in locally convex topological vector spaces is developed. An analog of Fej\'{e}r's theorem is proved for these series. The theory is applied to distributional solutions of Cauchy-Riemann equations to…
We propose and investigate a bi-infinite matrix approach to the multiplication and composition of formal Laurent series. We generalize the concept of Riordan matrix to this bi-infinite context, obtaining matrices that are not necessarily…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We give a necessary and sufficient condition for a type of generalized power series to be algebraic over the ring of power series with coefficients in a finite field. This result extend a classical theorem of Huang-Stefanescu.
We study sets of integers that can be defined by the vanishing of a generalised polynomial expression. We show that this includes sets of values of linear recurrent sequences of Salem type and some linear recurrent sequences of Pisot type.…
In this note, we study the generalized fraction properties and power series properties of $\mathcal{S}$-Noetherian rings. Actually, we investigate two questions proposed in [A. Dabbabi, A. Benhissi, Generalization of the $S$-Noetherian…
Taylor's and Laurent's expansions of $G$-monogenic mappings taking values in the algebra of complex quaternion are obtained and singularities of these mappings are classified.
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…
We consider series expansions in bases of classical orthogonal polynomials. When such a series solves a linear differential equation with polynomial coefficients, its coefficients satisfy a linear recurrence equation. We interpret this…
The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of…
We associate a formal power series with integer coefficients to a positive real number, we interpret this series as a "$q$-analogue of a real." The construction is based on the notion of $q$-deformed rational number introduced in…
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincar\'e…
There is a theory of continued fractions for Laurent series in x^{-1} with coefficients in a field F. This theory bears a close analogy with classical continued fractions for real numbers with Laurent series playing the role of real numbers…
General linear electrodynamics allow for an arbitrary linear constitutive relation between the field strength two-form and induction two-form density if crucial hyperbolicity and energy conditions are satisfied, which render the theory…
Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with…
We study Grothendieck rings (in the sense of logic) of fields. We prove the triviality of the Grothendieck rings of certain fields by constructing definable bijections which imply the triviality. More precisely, we consider valued fields,…
In this work, we define a more general family of polynomials in several variables satisfying a linear recurrence relation. Then we provide explicit formulas and determinantal expressions. Finally, we apply these results to recurrent…
I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present…
We give a criterion which characterizes a real multi-variate Laurent polynomial with full-dimensional smooth Newton polytope to have the property that all sufficiently large powers of the polynomial have fully positive coefficients. Here a…