Q-difference intertwining operators for Uq(sl(n)): general setting and the case n=3

Let\(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and 1≤p<∞. We consider the spaceHp(β) of all power series\(f(z) = \sum\limits_{n = 0}^\infty {\hat f(n)z^n } \) such that Σ|\(\Sigma |\hat f(n)|^p \beta (n)^p< \infty \)(n)|p β(np<∞. We investigate regions on which our formal power series represent bounded analytic functions.

Concurrent universal Padé approximation

We show that, under conditions about the microcharacteristic variety of a coherent $\cal D$ -module, the Cauchy problem is well-posed in the spaces of formal power series with Gevrey growth. We deduce that the filtration of the Irregularity Sheaf of a holonomic $\cal D$ -module, which we defined in a previous work, is preserved under inverse image if some rather general geometric conditions are fullfilled.

The Umbral Transfer-Matrix Method. I. Foundations

We use transfinite induction to show that if L is an epimorphism of a vector space V and maps a vector subspace W of V into a proper subspace of itself, then there is a smallest subspace E of V containing W such that L(E) E (or a minimal space of surjectivity or solvability) and we give examples where there are infinitely many distinct minimal spaces of solvability. We produce an example showing that if L 1 and L 2 are two epimorphisms of a vector space V which are endomorphisms of a proper subspace W of V such that LI(W) n L2(W is a proper subspace of W, then there may not exist a smallest subspace E of V containing W such that LI(E) E L2(E). While no nonconstant linear partial differential operator maps the field of meromorphic functions onto itself, we construct a locally convex topological vector space of formal power series containing the meromorphic functions such that every linear partial differential operator with constant coefficients maps this space linearly and continuously onto itself. Furthermore, we show that algebraically there is for every linear partial differential operator P(D) with constant coefficients a smallest extension E of the meromorphic functions in n complex variables, where

On a class of suboptimal controls for infinite-dimensional bilinear systems

Let $\{\beta(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers and $1 \leq p < \infty$. We consider the space $\ell^{p}(\beta)$ of all power series $f(z)\hskip-2pt =\hskip-2pt \sum^{\infty}_{n=0} \skew4\widehat{f}(n)z^{n}$ such that $\sum_{n=0}^{\inf

A de Branges-Beurling theorem for the full Fock space

In this chapter we shall consider the class of power series spaces. This is important since many spaces in analysis are isomorphic to power series spaces through classical series representations. At the same time this is a class of Fréchet spaces whose structure is fully understood.

We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on $$\Lambda _{1}(n)$$ Λ 1 ( n ) and $$\Lambda _{\infty }(n)$$ Λ ∞ ( n ) , and consequently on $$H(\mathbb {C})$$ H ( C ) and $$H(\mathbb {D})$$ H ( D ) .

Reduction of everywhere convergent power series with respect to Gröbner bases

On formal power series defined by infinite linear systems

For a positive integer n and a subset S⊆[n−1], the descent polytope DP S is the set of points (x 1,…,x n ) in the n-dimensional unit cube [0,1] n such that x i ≥x i+1 if i∈S and x i ≤x i+1 otherwise. First, we express the f-vector as a sum over all subsets of [n−1]. Second, we use certain factorizations of the associated word over a two-letter alphabet to describe the f-vector. We show that the f-vector is maximized when the set S is the alternating set {1,3,5,…}∩[n−1]. We derive a generating function for F S (t), written as a formal power series in two non-commuting variables with coefficients in ℤ[t]. We also obtain the generating function for the Ehrhart polynomials of the descent polytopes.

In this chapter we prepare the ground for the proof of the Jung-Abhyankar theorem in section 2 and the study of quasiordinary power series in section 4 of chapter V. We assume that the reader is acquainted with the notion of power series over a field; in section 1, for the convenience of the reader, we give some background, introduce convergent power series over the real and complex numbers in section 2, and prove Weierstraß division and preparation theorem in section 3. The category of formal (resp. analytic) algebras—these are homomorphic images of formal (resp. convergent) rings of power series—is treated in section 4. The last section considers, in particular, the completion of an analytic algebra; these results are needed to prove the convergent case of the Jung-Abhyankar theorem.

On etudie les espaces solution ponderes d'un systeme hypoelliptique P(D) d'equations aux derivees partielles a coefficients constants qui sont isomorphes a des espaces de series de puissances de type fini