Results 41 to 50 of about 5,160 (166)
A measure theoretic approach to Lipschitz regularity and its Haar type wavelet analysis
Mathematical Modelling and AnalysisThe $\alpha$−Lipschitz character of a time series or an image summarizes, in the single parameter α, some persistence properties of the original function modeling the given signal.
Hugo Aimar, Juliana Boasso
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On Natural Functions and Lipschitz Functions
Real Analysis Exchange, 2003 Let \(E\subset \mathbb R\) be a nonempty bounded set, let \(X\) be a metric space with metric \(d\). The total variation \(V(f,E)\) of a map \(f\colon~E\rightarrow X\) on \(E\) is defined as \[ V(f,E)=\sup~\left\{\sum_{i=1}^{m}d(f(t_i),f(t_{i-1 ...
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Superposition operator problems of Hölder-Lipschitz spaces
Demonstratio MathematicaLet ff be a function defined on the real line, and Tf{T}_{f} be the corresponding superposition operator which maps hh to Tf(h){T}_{f}\left(h), i.e., Tf(h)=f∘h{T}_{f}\left(h)=f\circ h. In this article, the sufficient and necessary conditions such that Tf{
Niu Yeli, Wang Heping
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Lipschitz Functions and Spectral Synthesis [PDF]
Proceedings of the American Mathematical Society, 1981 An S S -set in the circle group
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Density of Lipschitz functions in energy
Calculus of Variations and Partial Differential Equations, 2022 AbstractIn this paper, we show that the density in energy of Lipschitz functions in a Sobolev space$$N^{1,p}(X)$$N1,p(X)holds for all$$p\in [1,\infty )$$p∈[1,∞)whenever the spaceXis complete and separable and the measure is Radon and positive and finite on balls. Emphatically,$$p=1$$p=1is allowed.
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Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces
Abstract and Applied Analysis, 2014 We prove a quasiconformal analogue of Koebe’s theorem related to the average Jacobian and use a normal family argument here to prove a quasiregular analogue of this result in certain domains in n-dimensional space.
Miodrag Mateljević
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Regularity of Lipschitz Functions on the Line
Real Analysis Exchange, 2003 The authors note a gap in Sciffer's construction of an everywhere irregular Lipschitz function of the real line and give their own construction. The Dini derivatives are denoted by \(D^+\), \(D_+\), \(D^-\), \(D_-\). The Clarke derivatives are \(S^+f(x)=\limsup_{y\to x+,h\to0}(f(y+h)-f(y))/h\), \(S_+f(x)=\liminf_{y\to x+,h\to0}(f(y+h)-f(y))/h\), \(S^-f(
Preiss, David, Rolland, Louise
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Open MathematicsLet L=−△+VL=-\bigtriangleup +V be the Schrödinger operator on Rn{{\mathbb{R}}}^{n}, where V≠0V\ne 0 is a non-negative function satisfying the reverse Hölder class RHq1R{H}_{{q}_{1}} for some q1>n⁄2{q}_{1}\gt n/2. △\bigtriangleup is the Laplacian on Rn{{\
Celik Suleyman +2 more
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Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials
Journal of Inequalities and Applications, 2017 The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials.
Tarul Garg +2 more
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Peak Sets for Lipschitz Functions [PDF]
Proceedings of the American Mathematical Society, 1978 We study the peak sets for the algebras of functions analytic in the unit disc D and satisfying a Lipschitz condition on ∂
Novinger, W. P., Oberlin, D. M.
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