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Rough Isometries of Lipschitz Function Spaces
, 710
"... We show that rough isometries between metric spaces X,Y can be lifted to the spaces of real valued 1Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally enri ..."
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We show that rough isometries between metric spaces X,Y can be lifted to the spaces of real valued 1Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough isometries between X and Y can be reconstructed from structurally
Lipschitz Functions with Prescribed Derivatives and Subderivatives
, 1995
"... . In general it is difficult to construct Lipschitz functions which are not directly built up from either convex or distance functions. One impediment to such constructions is that outside of the real line it is difficult to find antiderivatives. The main result of this paper provides, under suitab ..."
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Cited by 11 (4 self)
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. In general it is difficult to construct Lipschitz functions which are not directly built up from either convex or distance functions. One impediment to such constructions is that outside of the real line it is difficult to find antiderivatives. The main result of this paper provides, under
Embeddings with a lipschitz function
 Random Structures and Algorithms
"... We investigate a new notion of embedding of subsets of {−1, 1} n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1,..., n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result is that ..."
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Cited by 1 (0 self)
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We investigate a new notion of embedding of subsets of {−1, 1} n in a given normed space, in a way which preserves the structure of the given set as a class of functions on {1,..., n}. This notion is an extension of the margin parameter often used in Nonparametric Statistics. Our main result
RICCI CURVATURE AND CONVERGENCE OF LIPSCHITZ FUNCTIONS
, 2010
"... We give a definition of convergence of differential of Lipschitz functions with respect to measured GromovHausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic cones of manifolds with nonnegative Ricci curvature and Euclidea ..."
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Cited by 4 (2 self)
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We give a definition of convergence of differential of Lipschitz functions with respect to measured GromovHausdorff topology. As their applications, we give a characterization of harmonic functions with polynomial growth on asymptotic cones of manifolds with nonnegative Ricci curvature
Pathological Lipschitz Functions in R N
"... In recent years four subdifferential maps have been widely used: the Clarke subdifferential, the MichelPenot subdifferential, the IoffeMordukhovich Kruger approximate subdifferential, and the Dini subdifferential. We denote these four notions by `C', `MP', `A', and `D' resp ..."
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' respectively. Each of them is a generalization from convex to locally Lipschitz functions and each of them generalizes different aspects of the convex situation. In this thesis, we construct Lipschitz functions with pathological properties and study the differences among these four subdifferential maps
Lipschitz Functions on Expanders are Typically Flat
"... This work studies the typical behavior of random integervalued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: MLipschitz functions (functions which change by at most M along edges) and integerhomomorphisms (functions which change ..."
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Cited by 2 (2 self)
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This work studies the typical behavior of random integervalued Lipschitz functions on expander graphs with sufficiently good expansion. We consider two families of functions: MLipschitz functions (functions which change by at most M along edges) and integerhomomorphisms (functions which change
Generalized Lipschitz functions Elyes Jouini
"... The aim of this paper is to establish a compactness result on some function sets. More precisely, our paper extends the concept of Lipschitz functions to a larger class including nondecreasing (nonnecessarily continuous) functions, functions with bounded below derivatives. We prove then that a bound ..."
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The aim of this paper is to establish a compactness result on some function sets. More precisely, our paper extends the concept of Lipschitz functions to a larger class including nondecreasing (nonnecessarily continuous) functions, functions with bounded below derivatives. We prove then that a
The Daugavet Property of the Space of Lipschitz Functions
"... Abstract. In this paper we will prove that the Banach space of Lipschitz functions on a compact convex set in a Banach space and the Banach space of continuously differentiable functions on a closure of some bounded domain in R n possess the Daugavet property. ..."
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Abstract. In this paper we will prove that the Banach space of Lipschitz functions on a compact convex set in a Banach space and the Banach space of continuously differentiable functions on a closure of some bounded domain in R n possess the Daugavet property.
CONSTRUCTIVE BOUNDED SEQUENCES AND LIPSCHITZ FUNCTIONS
"... Multiplier conditions equivalent to the constructive boundedness of a nonnegative real sequence M are derived. If the termwise product sM is bounded in sum whenever s is bounded in sum, then an upper bound for M can be constructed. One consequence is a constructive generalization of Fichtenholz&apo ..."
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's characterization of Lipschitz functions on metric spaces. The appropriate Lipschitz constants are constructed in the sense of Bishop's constructive mathematics. 1.
Results 11  20
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