Absolute and Square Summability & Integration of sinc function

1. What does square summable mean?
2. What is absolute summable?
3. How do you know if something is absolutely summable?
4. Is sinc absolutely summable?

What does square summable mean?

In mathematics, a square-integrable function, also called a quadratically integrable function or function or square-summable function, is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite.

What is absolute summable?

absolutely summable (not comparable) (mathematical analysis) Of an infinite series: such that the sum of the absolute values of its summands converges.

How do you know if something is absolutely summable?

Definition: Let be a normed linear space. A series in is said to be Absolutely Summable if the numerical series $\displaystyle\sum_i=1^\infty \| x_i \|$ converges. It is important to note that if we consider the with the Euclidean norm, then absolute summability and absolute convergence is equivalent.

Is sinc absolutely summable?

The sinc function is not absolutely summable. The proof is not too complicated, it only involves basic calculus, and you can find it in the references.