We show that a locally compact group G has equivalent right and left uniform structures if (and only if) the sets of bounded, complex-valued, right and left uniformly ...

Abstract: Questions of uniform approximation of continuous functions of bounded variation on ℝ n with the values in the Banach space are being studied by aggregates of summatory type constructed on ...

Let $X$ be a set, $A$ a family of real-valued functions on $X$ which contains the constants, $\mu_A$ the weak uniformity generated by $A$, and $U(\mu_AX)$ the ...

We show that the lateral regularizations of the generator of any uniformly bounded set-valued composition Nemytskij operator acting in the spaces of functions of bounded variation in the sense of ...

ABSTRACT: In the first part of this work, a convex partition of a compact subset is constructed. Minimum-length surrounding curve and minimum-area surrounding surfaces for a compact set are ...

Abstract: We consider deep neural networks (DNNs) with a Lipschitz continuous activation function and with weight matrices of variable widths. We establish a uniform convergence analysis framework in ...

Due to a planned power outage on Friday, 1/14, between 8am-1pm PST, some services may be impacted. A line drawing of the Internet Archive headquarters building façade. An illustration of a magnifying ...