Analysis Mathematica最新文献

It was a remarkable result of the last decades that every Banach space operator has an almost invariant half-space; see [1] and [17].Refining the technique used in [1], it has been shown quite recently that every operator (T) on a complex Hilbert space (mathcal{H}) has a diagonal operator inside itself; see [9].Applying this result to a block-triangular operator (Tinmathcal{L}(mathcal{H}_1 oplus mathcal{H}_2)),it can be proved that a translate of (T)is similar to an operator (widehat{T}inmathcal{L}(mathcal{H}^{(4)})) with two diagonal entries (D),(D_{*} ) and two entries (F), (F _{*} ) of rank (1).Given any operator (Q= [Q_{i,j}]_4)in the commutant ({widehat{T}}') of (widehat{T}), the operator entry (Q_{4,1}) intertwines (D) and (D _{*} ) up to a transformation of rank at most (2).The linear manifold of the operators (Q_{4,1}) is denoted by (mathcal{L}_{4,1}).The compressions of the transformations in (mathcal{L}_{4,1}) to a(3)-dimensional subspace form a subspace (mathcal{L} _{*} ) of the matrix algebra (M_3[mathbb{C}]).Transitivity properties of ({ T}') yield the transitivity of (mathcal{L} _{*} ).Our aim is to characterize all transitive subspaces (mathcal{L}) of (M_3[mathbb{C}]) obeying the transformation law derived from the intertwining condition on (mathcal{L}_{4,1}).In that way we obtain sufficient conditions for the existence of proper hyperinvariant subspaces of (T).

Quantitative versions of Helly's and Steinitz' theorems were first introduced by Bárány, Katchalski and Pach in 1982, and have grown into a well-studied field within discrete and convex geometry in the last decade. This note is an invitation to the field in the form of an incomplete collection of open problems.

The goal of this paper is to provide an expository description of a result of Carrasco Piaggio[8] connecting the Ahlfors regular conformal dimension of a compact uniformly perfect doubling metric space with the combinatorial (p)-moduli of the metric space. We give detailed construction of a metric associated with the (p)-modulus of the space when the (p)-modulus is zero, so that the constructed metric is in the Ahlfors regular conformal gauge of the metric space. To do so, we utilize the tools of hyperbolic filling, developed first in[10,6].

A (not necessarily closed) algebra of operators (mathcal{A}) on a Hilbert space is said to have the closability property if every densely defined linear transformation that commutes with (mathcal{A}) is closable. We show that an algebra of the form ({u(T):uin H^{infty}}), where T is an operator of class (C_{0}), has the closability property precisely when T has a certain finiteness property, usually know as property (P). An analogous result is proved for commutative von Neumann algebras.

New sufficient conditions for the uniform boundedness of the Steklov averaging operators in variable exponent spaces on the sets of infinite measure are obtained. In the spaces of periodic functions, the criterion is the known local analogue of the Muckenhoupt property. On the sets of infinite measure, it is not sufficient, and one must add a condition to control a function at infinity. In the present paper, we give such a condition, which weakens the known property of the logarithmic stabilization.

In this paper, we study the relationship between Sobolev extension domains and homogeneous Sobolev extension domains. Precisely, we obtain the following results,

• Let (1leq qleq pleq infty). Then a bounded ((L^{1, p}, L^{1, q}))-extension domain is also a ((W^{1, p}, W^{1, q}))-extension domain.

• Let (1leq qleq p<q ^{star} leq infty) or (n< q leq pleq infty). Then a bounded domain is a ((W^{1, p}, W^{1, q}))-extension domain if and only if it is an ((L^{1, p}, L^{1, q}))-extension domain.

• For (1leq q<n) and (q<nq ^{star} <pleq infty), there exists a bounded domain (Omegasubsetmathbb{R}^n) which is a ((W^{1, p}, W^{1, q}))-extension domain but not an ((L^{1, p}, L^{1, q}))-extension domain for (1 leq q <pleq n).

We show that under very mild conditions on a measure (mu) on the interval ([0,infty)), the span of ({x^k}_{k=n}^{infty}) is dense in (L^2(mu)) for any (n=0,1,ldots{}). We present two different proofs of this result, one based on the density index of Berg and Thill and one based on the Hilbert space (L^2(mu)oplus mathbb{C}^{n+1}). Using the index of determinacy of Berg and Durán we prove that if the measure (mu) on (mathbb{R}) has infinite index of determinacy then the polynomial ideal (R(x)mathbb{C}[x]) is dense in (L^2(mu)) for any polynomial R with zeros having no mass under (mu).

In this paper, we prove that if a commuting family of operators ( tau = (T_lambda)_{lambdainLambda}) on a Banach space (mathcal{X}) is Bochner integrable, then

This result extends the well-known theorem on the subadditivity of the spectral radius for a finite set of commuting operators. We also provide an example illustrating that Bochner integrability cannot be substituted by a weaker form of integrability.

We study the higher-order delay differential equation

where (k) is a positive integer, (a(z)) is a rational function and (R(z,w)) is rational in (w) with rational coefficients. We obtain necessary conditions on the degree of (R(z, w)) for this delay differential equation to admit subnormal transcendental meromorphic solutions. On the other hand, we obtain a reduced form of the equation above when (R(z,w)) becomes a rational function.