New posts in Analysis

Is "Convolution operator" well-defined and injective?

Let $|f(x)-f(y)| \leqslant (x-y)^2$ for all $x,y\in \mathbb{R}.$ Show that $f$ is a constant.

Show that $\int_0^a \frac{\sin x}{x} dx \leq 1+\log a$ for all $a \geq 1$

show that $\intop_{0}^{1}\frac{\sin^{2}\left(x\right)}{x^{2}}$ diverges

Condition to union of connected sets be connected

Prove $ \lim_{h\rightarrow 0}\frac{1}{h}\int_a^x[f(t+h)-f(t)]\mathrm{d}t=f(x)-f(a). $

Example of a basis which is not a Riesz basis?

Asking for reference for challenging problems for Functional Analysis 1st course

the limit of $\frac{1}{\sqrt{n}}(1+\frac{2}{1+\sqrt2}+\frac{3}{1+\sqrt2+\sqrt3}+\dots+\frac{n}{1+\sqrt2+\sqrt3+\dots+\sqrt n})$ as $n\to\infty$

Finding a rational number in between two rationals