Analysis Mathematica最新文献

The asymptotic study of a time-dependent function ƒ as the solution of a differential equation often leads to the question of whether its derivative (f') vanishes at infinity. We show that a necessary and sufficient condition for this is that (f') is what may be called asymptotically uniform. We generalize the result to higher order derivatives. We also show that the same property for ƒ itself is also necessary and sufficient for its one-sided improper integrals to exist. The article provides a broad study of such asymptotically uniform functions.

We construct a crystalline measure on the real line that is not aFourier quasicrystal.

We give a universal formula describing derivation operators on a Hilbert space for a large class of interpolation methods. It is based on a simple new technique on “critical points” where all the derivations attain the maximum. We deduce from this a version of Kalton uniqueness theorem for such methods, in particular, for the real method. As an application of our ideas is the construction of a weak Hilbert space induced by the real J-method. Previously, such space was only known arising from the complex method. To complete the picture, we show, using a breakthrough of Johnson and Szankowski, nontrivial derivations whose values on the critical points grow to infinity as slowly as we wish.

The p-Dunford–Pettis relatively compact property ((1le p<infty))is studied in individual Banach spaces and in spaces of operators. The questionof whether a space of operators has the p-Dunford–Pettis relatively compactproperty is studied using Dunford–Pettis p-convergent evaluation operators.

We characterize the good weights for some weighted weak-type iterated Hardy-Copson inequalities to hold.

We investigate an integral operator (T_{t,lambda}) which preservesthe Carleson measure for the Möbius invariant Besov space (B_p) on the unit ball of (mathbb{C}^{n}). A holomorphic function space (W_beta^p), associated with the Carleson measure for (B_p), is introduced. As applications for the operator (T_{t,lambda}), we estimate the distance from Bloch-type functions to the space (W_beta^p), which extends Jones' formula. Moreover, the bounded small Hankel operators on (B_p) and the atomic decomposition of (W_beta^p) are characterized.

In this article some results on the value distribution theory of analyticfunctions defined in angles of (mathbb{C}), due mainly to B. Ja. Levin and A. Pfluger,will be extended to the more general situation where the functions are defined inangles of (mathbb{C}backslash{ 0}). More precisely, angles (S ( theta_{1},theta_{2}) ) with vertex at the origin will beconsidered and where a singularity at zero is allowed. An special class of thesefunctions are those of completely regular growth for which it is proved a basic resultwhich yields an expression of the density of its zeros in terms of the indicatorfunction.

Suppose that (T) is an absolutely continuous polynomially bounded operator, (S_{omega}) is a bilateral weighted shift, there exists a (phiin mathbb{H}^{infty}) such that (ker phi(S_{omega}^{*})neq {0}) and a nonzero operator (X) such that (S^{(infty)}_{omega}X=XT), where (S^{(infty)}_{omega}) is the infinite countable orthogonal sum of copies of (S_{omega}). We prove that (T) has nontrivial hyperinvariant subspaces, that are the closures of (text{Ran} psi(T)) for some (psi in mathbb{H}^{infty}).

The set of smooth functions is not dense in Morrey spaces. To address the density issue in Morrey spaces, Zorko spaces are defined by utilizing the difference of a function of first order. In this paper, we propose a subspace of Morrey spaces which is defined using the difference of a function of second order. Approximation properties in the new subspace are investigated and the relation with Zorko spaces is studied via properties of smoothness spaces.

In this paper, a decomposition theorem for (covariant) unitarygroup representations on Kaplansky–Hilbert modules over Stone algebras is established,which generalizes the well-known Hilbert space case (where it coincideswith the decomposition of Jacobs, deLeeuw and Glicksberg).

The proof rests heavily on the operator theory on Kaplansky–Hilbert modules,in particular the spectral theorem for Hilbert–Schmidt homomorphisms onsuch modules.

As an application, a generalization of the celebrated Furstenberg–Zimmerstructure theorem to the case of measure-preserving actions of arbitrary groupson arbitrary probability spaces is established.