Displaying similar documents to “Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces”

On extended eigenvalues and extended eigenvectors of truncated shift

Hasan Alkanjo (2013)

Concrete Operators

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In this paper we consider the truncated shift operator Su on the model space K2u := H2 θ uH2. We say that a complex number λ is an extended eigenvalue of Su if there exists a nonzero operator X, called extended eigenvector associated to λ, and satisfying the equation SuX = λXSu. We give a complete description of the set of extended eigenvectors of Su, in the case of u is a Blaschke product..

Resistance Conditions and Applications

Juha Kinnunen, Pilar Silvestre (2013)

Analysis and Geometry in Metric Spaces

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This paper studies analytic aspects of so-called resistance conditions on metric measure spaces with a doubling measure. These conditions are weaker than the usually assumed Poincaré inequality, but however, they are sufficiently strong to imply several useful results in analysis on metric measure spaces. We show that under a perimeter resistance condition, the capacity of order one and the Hausdorff content of codimension one are comparable. Moreover, we have connections to the Sobolev...

Musielak-Orlicz-Hardy Spaces Associated with Operators Satisfying Reinforced Off-Diagonal Estimates

The Anh Bui, Jun Cao, Luong Dang Ky, Dachun Yang, Sibei Yang (2013)

Analysis and Geometry in Metric Spaces

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Let X be a metric space with doubling measure and L a one-to-one operator of type ω having a bounded H∞ -functional calculus in L2(X) satisfying the reinforced (pL; qL) off-diagonal estimates on balls, where pL ∊ [1; 2) and qL ∊ (2;∞]. Let φ : X × [0;∞) → [0;∞) be a function such that φ (x;·) is an Orlicz function, φ(·;t) ∊ A∞(X) (the class of uniformly Muckenhoupt weights), its uniformly critical upper type index l(φ) ∊ (0;1] and φ(·; t) satisfies the uniformly reverse Hölder inequality...

Nonexistence Results for Semilinear Equations in Carnot Groups

Fausto Ferrari, Andrea Pinamonti (2013)

Analysis and Geometry in Metric Spaces

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In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot groups of arbitrarly large step. Moreover, we prove some nonexistence results for semilinear equations in the Engel group, which is the simplest Carnot group that is not of type ★.

On Asymmetric Distances

Andrea C.G. Mennucci (2013)

Analysis and Geometry in Metric Spaces

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In this paper we discuss asymmetric length structures and asymmetric metric spaces. A length structure induces a (semi)distance function; by using the total variation formula, a (semi)distance function induces a length. In the first part we identify a topology in the set of paths that best describes when the above operations are idempotent. As a typical application, we consider the length of paths defined by a Finslerian functional in Calculus of Variations. In the second part we generalize...

Modeling the tip-sample interaction in atomic force microscopy with Timoshenko beam theory

Julio R. Claeyssen, Teresa Tsukazan, Leticia Tonetto, Daniela Tolfo (2013)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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A matrix framework is developed for single and multispan micro-cantilevers Timoshenko beam models of use in atomic force microscopy (AFM). They are considered subject to general forcing loads and boundary conditions for modeling tipsample interaction. Surface effects are considered in the frequency analysis of supported and cantilever microbeams. Extensive use is made of a distributed matrix fundamental response that allows to determine forced responses through convolution and to absorb...

Compactness of Special Functions of Bounded Higher Variation

Luigi Ambrosio, Francesco Ghiraldin (2013)

Analysis and Geometry in Metric Spaces

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Given an open set Ω ⊂ Rm and n > 1, we introduce the new spaces GBnV(Ω) of Generalized functions of bounded higher variation and GSBnV(Ω) of Generalized special functions of bounded higher variation that generalize, respectively, the space BnV introduced by Jerrard and Soner in [43] and the corresponding SBnV space studied by De Lellis in [24]. In this class of spaces, which allow as in [43] the description of singularities of codimension n, the distributional jacobian Ju need not...

Neighborhood base at the identity of free paratopological groups

Ali Sayed Elfard (2013)

Topological Algebra and its Applications

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In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.

Bayesian Analysis for Robust Synthesis of Nanostructures

Nader Ebrahimi, Mahmoud Shehadeh, Kristin McCullough (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

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Nanomaterials, because of their unique properties such as extremely small size and increased ratio of surface area to volume, have a great potential in many industrial applications that involve electronics, sensors, solar cells, super-strong materials, coatings, drug delivery, and nanomedicine. They have the potential also to improve the environment by direct applications of these materials to detect, prevent and remove pollutants. While nanomaterials present seemingly limitless possibilities,...

The Lusin Theorem and Horizontal Graphs in the Heisenberg Group

Piotr Hajłasz, Jacob Mirra (2013)

Analysis and Geometry in Metric Spaces

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In this paper we prove that every collection of measurable functions fα , |α| = m, coincides a.e. withmth order derivatives of a function g ∈ Cm−1 whose derivatives of order m − 1 may have any modulus of continuity weaker than that of a Lipschitz function. This is a stronger version of earlier results of Lusin, Moonens-Pfeffer and Francos. As an application we construct surfaces in the Heisenberg group with tangent spaces being horizontal a.e.

Are law-invariant risk functions concave on distributions?

Beatrice Acciaio, Gregor Svindland (2013)

Dependence Modeling

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While it is reasonable to assume that convex combinations on the level of random variables lead to a reduction of risk (diversification effect), this is no more true on the level of distributions. In the latter case, taking convex combinations corresponds to adding a risk factor. Hence, whereas asking for convexity of risk functions defined on random variables makes sense, convexity is not a good property to require on risk functions defined on distributions. In this paper we study the...