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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… (More)

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk D in C arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely… (More)

—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… (More)

1. INTRODUCTION. The delight of finding unexpected connections is one of the rewards of studying mathematics. In this paper we present connections that link the following seven superficially unrelated entities:

Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D. The number ßf(z) represents the maximum dilation of / at z. The set consisting of all ß/(z), for z e D… (More)

Let ϕ be a holomorphic self-map of a bounded homogeneous domain D in C n. In this work, we show that the composition operator Cϕ : f → f • ϕ is bounded on the Bloch space B of the domain and provide estimates on its operator norm. We also give a sufficient condition for ϕ to induce an isometry on B. This condition allows us to construct non-trivial examples… (More)

Let ϕ be an analytic self-map of the open unit disk D in the complex plane C and let u be a fixed analytic function on D. The weighted composition operator is defined on the space H(D) of analytic functions on D by uCϕf = u · (f • ϕ), f ∈ H(D). In this work, we characterize the bounded and the compact weighted composition operators from the Besov spaces Bp… (More)

In this paper, we establish bounds on the norm of multiplication operators on the Bloch space of the unit disk via weighted composition operators. In doing so, we characterize the isometric multiplication operators to be precisely those induced by constant functions of modulus 1. We then describe the spectrum of the multiplication operators in terms of the… (More)

We study the potential theory of trees with nearest-neighbor transition probability that yields a recurrent random walk and show that, although such trees have no positive potentials, many of the standard results of potential theory can be transferred to this setting. We accomplish this by defining a non-negative function H, harmonic outside the root e and… (More)