# Questions tagged [uniform-convergence]

For sequences of functions, uniform convergence is a mode of convergence stronger than pointwise convergence, preserving certain properties such as continuity. This tag should be used with the tag [convergence].

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### Does there exist the following theorem for complex case?

‎Consider the following theorem (see theorem 7.17 of [W. Rudin. Priniciples of Mathematical Analysis, Mcgraw-Hilly, 1976.])‎ Theorem. Suppose ‎$‎\{f_n\}‎$ ‎is ‎sequence ‎of ‎functions, ‎differentiable ...
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### uniform convergence of cesaro sums of fourier series

Can someone help me with this exercise? Let f be a 1-periodic and continuous function in $\mathbb{R}$ .Show that $\sigma_{n}(f)(x)\xrightarrow{n\to \infty} f(x)$ uniformly in the interval [0,1) where ...
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### How can I prove the stability of this system? [closed]

Consider the following system: $\dot{x}_1=x_2$ $\dot{x}_2=-x_2-sgn(x_1)$ where sgn(.) is the sign function. In simulations, both $x$ and its derivative converge to zero but I can not prove it ...
From mono-dimensional theory of function series, we know that the following term by term differentiation theorem holds: Theorem 1. Suppose that $u_k : [a, b]\to \mathbb{R}$, for each $k = 1, 2,\dots$, ...