In this paper we consider analytical functions of unbounded type on Banach spaces. We are interested in finding under which conditions a given sequence polynomials supports entire type. Some relevant counterexamples indicated. show if X is an infinite dimensional space, then H(x) \ Hb(X) can be represented as union linear subspaces (without the origin).

Mφ : H → H for φ ∈ H∞(Ω). We mention some known results in this area that serve as a motivation for the present paper. First, if H is the classical Hardy space of the unit disk D, and if φ is an inner function on D, then Mφ is a pure isometry and a shift operator on H , and so its reducing subspaces are in a one-to-one correspondence with the closed subspaces of H (φH). Therefore, the reducing ...

We consider the use of low-dimensional linear subspace models to infer one high-dimensional signal from another, for example, predicting an image sequence from a related image sequence. In the memoryless case the subspaces are found by rank-constrained division, and inference is an inexpensive sequence of projections. In the finite-memory case, the subspaces form a linear dynamical system that ...

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...

Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos (GLTR) method is well-known type approach for solving large-scale TRS. projects original TRS onto sequence of lower dimensional Krylov subspaces, whose orthonormal bases are generated by symmetric process, computes approximate solutions from underlying subspa...

let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...

In this paper we investigate Bessel sequences in the space L2(R s), in Sobolev spaces Hμ(Rs) (μ > 0), and in Besov spaces B μ p,p(R s) (1 p ∞). For each j ∈ Z, let Ij be a countable index set. Let (ψj,α)j∈Z, α∈Ij be a family of functions in L2(R). We give some sufficient conditions for the family to be a Bessel sequence in L2(R s) or Hμ(Rs). The results obtained in this paper are useful for the...