everywhere smooth function
1Non-analytic smooth function — In mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not …
2Smooth coarea formula — In Riemannian geometry, the smooth coarea formulas relate integrals over the domain of certain mappings with integrals over their codomains.Let scriptstyle M,,N be smooth Riemannian manifolds of respective dimensions scriptstyle m,geq, n. Let… …
3Dirac delta function — Schematic representation of the Dirac delta function by a line surmounted by an arrow. The height of the arrow is usually used to specify the value of any multiplicative constant, which will give the area under the function. The other convention… …
4Generalized function — In mathematics, generalized functions are objects generalizing the notion of functions. There is more than one recognised theory. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and (going …
5Maximal function — Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability… …
6Differentiable function — A differentiable function The absolute value function is not …
7Sinc function — In mathematics, the sinc function, denoted by scriptstylemathrm{sinc}(x), and sometimes as scriptstylemathrm{Sa}(x),, has two definitions, sometimes distinguished as the normalized sinc function and unnormalized sinc function. In digital signal… …
8Analytic function — This article is about both real and complex analytic functions. The article holomorphic function is solely about analytic functions in complex analysis. An analytic signal is a signal with no negative frequency components. In mathematics, an… …
9Lacunary function — In analysis, a lacunary function, also known as a lacunary series, is an analytic function that cannot be analytically continued anywhere outside the circle of convergence within which it is defined by a power series. The word lacunary is derived …
10Sign function — In mathematics, the sign function is a mathematical function that extracts the sign of a real number. To avoid confusion with the sine function, this function is often called the signum function (after the Latin form of sign ).In mathematical… …
