We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.

No abstract

In this paper, we study the multiplication operators on the space of complex-valued functions f on the set of vertices of a rooted infinite tree T which are Lipschitz when regarded as maps between metric spaces. The metric structure on T is induced by the distance function that counts the number of edges of the unique path connecting pairs of vertices, while the metric on C is Euclidean. After observing that the space L of such functions can be endowed with a Banach space structure, we characterize the multiplication operators on L that are bounded, bounded below, and compact. In addition, we establish estimates on the operator norm and on the essential norm, and determine the spectrum. We then prove that the only isometric multiplication operators on L are the operators whose symbol is a constant of modulus one. We also study the multiplication operators on a separable subspace of L we call the little Lipschitz space. Mathematics Subject Classification (2000). Primary 47B38, 05C05.

In this paper, we characterise the analytic functions

-¥ f o

1, and

No abstract

We have investigated the molecular mechanisms that produce different structural and functional behavior in the monomeric and trimeric forms of seminal vesicle protein no. 4, a protein with immunomodulatory, anti-inflammatory, and procoagulant activity secreted from the rat seminal vesicle epithelium. The monomeric and trimeric forms were characterized in solution by CD. Details of the self-association process and structural changes that accompany aggregation were investigated by different experimental approaches: trypsin proteolysis, sequence analysis, chemical modification, and computer modeling. The self-association process induces conformational change mainly in the 1-70 region, which appears to be without secondary structure in the monomer but contains a-helix in the trimer. In vivo, proteolysis of seminal vesicle protein no. 4 generates active peptides and this is affected by the monomer/trimer state, which is regulated by the concentration of the protein. The information obtained shows how conformational changes between the monomeric and trimeric forms represent a crucial aspect of activity modulation.

Abstract. In this paper, we introduce and study polyharmonic functions on trees. We prove that the discrete version of the classical Riquier problem can be solved on trees. Next, we show that the discrete version of a characterization of harmonic functions due to Globevnik and Rudin holds for biharmonic functions on trees. Furthermore, on a homogeneous tree we characterize the polyharmonic functions in terms of integrals with respect to finitely-additive measures (distributions) of certain functions depending on the Poisson kernel. We define polymartingales on a homogeneous tree and show that the discrete version of a characterization of polyharmonic functions due to Almansi holds for polymartingales. We then show that on homogeneous trees there are 1-1 correspondences among the space of nth-order polyharmonic functions, the space of nth-order polymartingales, and the space of n-tuples of distributions. Finally, we study the boundary behavior of polyharmonic functions on homogeneous trees whose associated distributions satisfy various growth conditions.

In this work we solve the extremal problem of characterizing all bounded analytic functions f: Δ → C (where Δ is the open unit disk) for which the Bloch constant βf = sup{(1−|z|2)|f′(z)|: z ε Δ is a bound. Normalizing, we study f: Δ → Δ with βf = 1. We show that these are precisely the conformal automorphisms of Δ together with those functions whose zeros form an infinite sequence (zn)nεN such that lim supn→∞|g(zn)|Πk≠nzn−zk1−znzk=1, where g is the non‐vanishing function such that f/g is a Blaschke product. In particular, non‐vanishing inner functions, finite Blaschke products, and outer functions for the class H∞(Δ) with image contained in Δ are not extremal functions.