Sentence examples for uniform norms from inspiring English sources
Here ∥⋅∥0,a and ∥⋅∥0,b are certain weighted uniform norms.
We start with the Kolmogorov type inequality between the uniform norms of the Marchaud fractional derivative of a function, the function itself and its higher-order derivative.
From the result (2.2) we conclude that, if 6-convex functions are closed in uniform norms, then their third derivatives are also closed in weighted (L^{2} -norm.
Specifically, we focus on inequalities between the uniform norms of the function and its derivatives; the uniform norms of the function and its intermediate derivative and the norm of its higher-order derivative in the ideal lattice; the norms of the function and its derivatives in the ideal lattice.
Then in Section 3.3 we give another extension of results of Section 3.1 on the case of inequalities between the uniform norms of the Marchaud fractional derivative of a function, the uniform norm of the function itself, and the norm of the higher-order derivative in an ideal lattice.
About South America, the Pan American Health Organization is promoting scientific research, often in the form of epidemiologic studies, in order to propose uniform norms and standards.
The Chebyshev norm is also called the norm, uniform norm, minimax norm, or simply the maximum absolute value.
We study the estimation of a regression function f in the uniform norm assuming that f belongs to a Hölder class.
This is done both when the group is endowed with the topology of pointwise norm-convergence and the topology of uniform norm-convergence.
The formulas for the rate functions of the pointwise difference and the uniform norm of the difference are expressed in terms of the underlying density function and their asymptotics are found.
Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein Uhlenbeck processes is discussed.
