Results 231 to 240 of about 3,827,469 (279)

Fourier transforms in generalized Lipschitz classes

Proceedings of the Steklov Institute of Mathematics, 2013
We obtain sufficient conditions for the Fourier transform of a function f ∈ L1(ℝ) to belong to generalized Lipschitz classes defined by the modulus of smoothness of order m. The sharpness of these conditions is established in the cases when f(t) ≥ 0 on ℝ or tf (t) ≥ 0 on ℝ.
S. S. Volosivets, B. I. Golubov
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Lipschitz Metrics for a Class of Nonlinear Wave Equations

, 2015
The nonlinear wave equation $${u_{tt}-c(u)(c(u)u_x)_x=0}$$utt-c(u)(c(u)ux)x=0 determines a flow of conservative solutions taking values in the space $${H^1(\mathbb{R})}$$H1(R). However, this flow is not continuous with respect to the natural H1 distance.
A. Bressan, Geng Chen
semanticscholar   +1 more source

Lipschitz classes and convolution approximation processes

Mathematical Proceedings of the Cambridge Philosophical Society, 1981
For a continuous function f(x) on the reals or on the circle T (continuous and 2π periodic) we say that f(x) belongs to the generalized Lipschitz class, denoted by f ∈ Lip* α, ifwhere and Δhf(x) = f(x + ½h)−f(x−½h). For a convolution approximation process given bywherewe shall investigate equivalence relations between the asymptotic behaviour of (d/dx)
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Singular Integral Operator Involving Higher Order Lipschitz Classes

Mediterranean Journal of Mathematics, 2017
As in [\textit{R. Abreu-Blaya} et al., Bull. Braz. Math. Soc. (N.S.) 48, No. 2, 253--260 (2017; Zbl 1375.30061)] the poly-analytic Cauchy integral is extended to higher-order Lipschitz classes for simply connected plane domains with smooth boundary. Concentrating on the bi-analytic case the boundary integral with the Bitsadze kernel rather than the ...
Juan Bory-Reyes, Lianet De la Cruz-Toranzo, Ricardo Abreu-Blaya   +2 more
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Boundary interpolation in weak Lipschitz classes

Journal of Mathematical Sciences, 2009
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Lipschitz classes on finite dimensional groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1969
In this paper G will denote a compact metric Abelian group having finite topological dimension, dim G. The discrete dual group of G will be denoted by Γ. The metric on G will be denoted by d(x, y), or |x-y| since translation-invariance is assumed.
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Bernstein-type operators, convexity and Lipschitz classes

Approximation Theory and its Applications, 1995
The authors study the monotonicity properties of the sequences of some Bernstein-type operators, relative to convex functions, as well as the preservation properties of Lipschitz classes for these operators. They start from a class of Bernstein-Schnabl type operators and give several illustrations for the operators of Bernstein, Stancu and Cheney ...
DELLA VECCHIA, Biancamaria, I. Rasa
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Rational approximation to Lipschitz and Zygmund classes

Constructive Approximation, 1992
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Borwein, P. B., Zhou, S. P.
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Lipschitz classes on 0-dimensional groups

Mathematical Proceedings of the Cambridge Philosophical Society, 1967
1. Let G be a compact metric 0-dimensional Abelian group. Its dual or character group Γ is a discrete countable torsion group. We denote elements of G by x, of Γ by y, the value of the character y at x by (x, y), and the Fourier transform of f by
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Specific properties of Lipschitz class functions

Acta Mathematica Hungarica
The authors find two conditions on an orthonormal system (ONS) in \( L_2(0,1) \) which imply that for arbitrary \( f \in\) Lip 1 and for any \( \varepsilon\in (0,1) \) the series \[\sum_{k=1}^{\infty} C_k^2(f)k^{2(1-\varepsilon)}\] converges (here \( C_k(f) \) are the Fourier coefficients with respect to that ONS).
Kashibadze, A., Tsagareishvili, V.
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