Analysis Mathematica最新文献

We characterize finite functions in the vector lattice (C(X)) of realcontinuous functions on a normal topological space (X). As an application, wegive a description of self-majorizing functions of (C(X)).

A (lambda)-graph system is a labeled Bratteli diagram with certain additional structure, which presents a subshift. The class of the (C^{*})-algebras (mathcal{O}_ mathfrak{L}) associated with (lambda)-graph systems is a generalized class of the class of Cuntz–Krieger algebras. In this paper, we will compute the strong extension groups( Ext _{rm s} (mathcal{O}_ mathfrak{L}))for the (C^*)-algebras associated with (lambda)-graph systems ( mathfrak{L} ) and study their relation with the weak extension group ( Ext _{rm w} (mathcal{O}_ mathfrak{L})).

Some selected open problems are displayed, with relevant results, comments and references. We focus on the classical Banach spaces (c_0), (l_1) and (l_infty).

In this paper, our main purpose is to establish a weak factorization of the classical Hardy spaces in terms of a multilinear Calderón-Zygmund operator on the ball Banach function spaces. Furthermore, a new characterization of the BMO space via the boundedness of the commutator generated by the multilinear Calderón-Zygmund operator is also obtained. The results obtained in this paper have generality. As examples, we apply the above results to weighted Lebesgue space, variable Lebesgue space, Herz space, mixed-norm Lebesgue space, Lorentz space and soon.

In this paper, we investigate some delay differential equations, and obtain some results on value distribution, such as poles and fixed points of transcendental meromorphic solutions (w(z)) with hyper order strictly less than 1, and their differences (Delta w(z)).

We proved that a map on bounded balanced pseudoconvex domainswhose Shilov boundaries are transitive under the isotropy groups of 0 isCarathéodory extremal map if and only if it is the extremal map of the squeezingfunction at the origin, and we also obtain the formulas of these two extremal mapswhich are unique up to unitary linear transformations. Especially, all of these twoextremal maps are non-singular linear transformations. Then we generalize theabove results to balanced domains with center at nonzero points.

We study the spectrality of a class of self-affine measures (mu_{M,D}) generated by an expanding matrix (Min M_{n}(mathbb{Z})) and a finite collinear digit set ({Dsubset mathbb{R}^{n}}). For the general form of the characteristic polynomial of (M), we analyze the relation between its roots and coefficients, and then give a method to find out a spectrum for (mu_{M,D}) by constructing a similarity transformation. This offers a fresh perspective on constructing a spectrum for (mu_{M,D}) on (mathbb{R}^{n}). Under a suitable condition, we also obtain a necessary and sufficient condition for self-affine measures with three-element collinear digit set on (mathbb{R}^{n}) to be spectral measures, and then construct a counterexample to a conjecture of Liu et al.

We prove some new bounds and continuity for the derivatives of higherorder multilinear maximal commutators and their fractional variants,both in the centered and in the uncentered cases. The main resultsrelated to the uncentered case are new even in the linear case. Ourmain results not only represent multilinear extension of the main results of [23] but also answer a questionoriginally proposed by the first author and Ma in [23].

In this paper, we will consider two notions of an invariant subspace for a linear relation: the first one is through the graph of a linear relation, and the second one is by using the resolvent function of a linear relation. Through some examples and preliminary results, it is shown that the second notion is more suitable when the spectral properties of liner relations are involved. In the second part of the paper, such a notion of an invariant subspace is allowed to develop, in a constructive way, the concept of group inverse for linear relations.

This paper characterizes the entire solutions of the following eiconal type partial differential equations

and

where p is a polynomial in (mathbb{C}^2), and (a_{0},a_{1},a_{2}) are constants in (mathbb{C}). Descriptions are given and complemented by various examples.