...dy of partial differential equations, the calculus of variations, harmonic analysis, and fractals.
...References|[a9]]] discusses applications of some of the ideas of geometric measure theory in the theory of Sobolev spaces and functions of bounded variation.
21 KB (3,319 words) - 17:46, 1 July 2020
there exists a non-trivial measure $ \mu $
Such a measure is called a [[Haar measure|Haar measure]]. It is unique up to multiplication by a constant.
14 KB (2,197 words) - 16:40, 31 March 2020
$#C+1 = 165 : ~/encyclopedia/old_files/data/W097/W.0907760 White noise analysis
...developed into a viable framework for stochastic and infinite-dimensional analysis [[#References|[a4]]]–[[#References|[a6]]], with a growing number of appli
27 KB (3,916 words) - 19:20, 13 January 2024
...ise. As in the case of, e.g., Banach algebras (cf. [[Banach algebra|Banach algebra]]), where the Gel'fand representation provides an answer, one asks whether
...in measure theory and the [[Poisson formula|Poisson formula]] for bounded harmonic functions on an open disc are special cases of the spectral theorem. The Fr
14 KB (2,252 words) - 08:09, 21 January 2024
...erator. In particular, the set of all nuclear operators is an ideal in the algebra $ L ( E) $;
Suppose that the algebra $ S ( E) $
24 KB (3,574 words) - 18:23, 21 January 2021
.... Even though aviation is more than 50 years old, an instrument that would measure the disturbance of the attack angle of the aircraft wing or the altitude of
...automatic control. In particular, one may mention the methods of frequency analysis; methods based on the first approximation to [[Lyapunov stability theory|Ly
43 KB (6,618 words) - 07:32, 26 March 2023