...role in various problems of boundary properties of functions, in
harmonic analysis, in the theory of power series, linear operators, random processes, and in
...g/legacyimages/h/h046/h046320/h04632085.png" /> is a non-negative singular
measure on <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.or
37 KB (5,073 words) - 18:20, 1 December 2014
...ences|[a3]]], W. Arveson [[#References|[a1]]] generalized and expanded the analysis just presented to cover cases when an arbitrary locally compact [[Abelian g
b) $\mathcal{X}$ is a [[C*-algebra|$C ^ { * }$-algebra]] and $\{ U _ { t } \} _ { t \in G }$ is a strongly continuous representati
14 KB (2,151 words) - 17:43, 1 July 2020
...algebra]]). The most important among these is the symmetric Banach measure algebra $ M (G) $
the algebra of all regular Borel measures on $ G $
20 KB (2,775 words) - 16:40, 31 March 2020
..., space of]]). An early construction of a non-associative, non-commutative algebra was given by H. König [[#References|[a6]]]. The main current (2000) direct
...f. also [[Net (directed set)|Net (directed set)]]) converging to the Dirac measure in $\mathcal{D} ^ { \prime } ( \mathbf{R} ^ { n } )$ (cf. also [[Generalize
12 KB (1,717 words) - 17:43, 1 July 2020
of square-summable functions with respect to the Haar measure on $ G $(
the measure of the entire group is taken to be 1). The algebra of all complex-valued representation functions on $ G $,
6 KB (855 words) - 16:40, 31 March 2020
...Further, between the non-degenerate symmetric representations of the group algebra $ L _ {1} ( G) $(
constructed with the left Haar measure) and the continuous unitary representations of the group $ G $
24 KB (3,516 words) - 08:27, 6 June 2020
[[Category:Classical measure theory]]
The term Hausdorff measures is used for a class of [[Outer measure|outer measures]] (introduced for the first time by Hausdorff in {{Cite|Ha}}
10 KB (1,546 words) - 09:43, 16 August 2013
algebra $ \mathfrak B $
of subsets and a probability measure $ \mu $
7 KB (970 words) - 08:09, 6 June 2020
...al group, then $C ^ { * } ( G )$ is isometrically isomorphic to the Banach algebra $C _ { 0 } ( \hat { G } ; \mathbf{C} )$ of all complex-valued continuous fu
...l norm and the pointwise product on $G$, $B ( G )$ is a commutative Banach algebra [[#References|[a4]]].
7 KB (1,059 words) - 15:30, 1 July 2020
...abstract|Harmonic analysis, abstract]]; [[Topological algebra|Topological algebra]]).
...he homomorphisms which are usually considered are those with values in the algebra $ C ( E) $
32 KB (4,602 words) - 04:46, 7 January 2022
...gebra $ A $ (cf. [[Algebra of functions|Algebra of functions]]) into the algebra $ L ( X) $
A functional calculus is one of the basic tools of general spectral analysis and the theory of Banach algebras and it enables one to use function-analyt
11 KB (1,521 words) - 02:23, 16 June 2022
...in abstract harmonic analysis (cf. [[Harmonic analysis, abstract|Harmonic analysis, abstract]]).
is a locally compact space with a measure $ m $,
30 KB (4,254 words) - 17:53, 13 January 2024
...><TR><TD valign="top">[7]</TD> <TD valign="top"> K. Yosida, "Functional analysis" , Springer (1980) pp. Chapt. 8, Sect. 4; 5</TD></TR><TR><TD valign="top"
...a3]]], Sect. 41. The basic observation is that the [[Banach algebra|Banach algebra]] of (continuous) almost-periodic functions on a (topological) group $ G
12 KB (1,716 words) - 11:05, 10 May 2020
''measure of a set''
...f a set for some mass distribution throughout the space. The notion of the measure of a set arose in the theory of functions of a real variable in connection
46 KB (7,065 words) - 19:30, 1 January 2021
A [[Topological algebra|topological algebra]] $A$ over the field of complex numbers whose topology is
elements being separately continuous for both factors. A Banach algebra is said to be commutative if
14 KB (2,346 words) - 22:48, 29 November 2014
...d out an analogue of the parametrization (in terms of zeros and a singular measure on the circle) of an inner function for the matrix-valued case. It turns ou
...ions to more abstract [[Harmonic analysis|harmonic analysis]] and function-algebra settings. A more delicate Beurling–Lax representation theorem has been sh
12 KB (1,802 words) - 17:01, 1 July 2020
such that the [[Lie algebra|Lie algebra]] $ \mathfrak g $
is the Lie algebra of $ H $
20 KB (2,996 words) - 08:42, 16 December 2019
...then given $f \in L ^ { 1 } ( \mu )$ one can find a set of full [[Measure|measure]] $X _ { f }$ such that for $x$ in this set the averages
==Wiener–Wintner return-time theorem and the Conze–Lesigne algebra.==
9 KB (1,431 words) - 17:03, 1 July 2020
of terms of the [[Harmonic series|harmonic series]]
In mathematical analysis both convergent and divergent series are used. For the latter various metho
29 KB (4,393 words) - 19:21, 27 January 2020
...s a role in very diverse branches of mathematics and physics, above all in analysis and its applications.
...n algebra; in analytic geometry it includes coordinate transformations; in analysis it includes differential and integral transforms and the Fourier integral.
67 KB (9,247 words) - 17:12, 29 October 2017