"'''Measure algebra'''" may refer to:
...l group with the operation of convolution; see [[measure algebra (harmonic analysis)]];
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$#C+1 = 37 : ~/encyclopedia/old_files/data/A011/A.0101390 Algebra of measures,
''measure algebra''
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...roup $G$: If $x$ is a function on $G$, summable with respect to the [[Haar measure]], whose Fourier transform does not vanish on the group of characters $\hat
This theorem is based on the regularity of the [[group algebra]] of a commutative locally compact group, and on the possibility of [[spect
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$#C+1 = 49 : ~/encyclopedia/old_files/data/Q076/Q.0706560 Quasi\AAhinvariant measure
A measure on a space that is equivalent to itself under "translations" of this spac
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$#C+1 = 38 : ~/encyclopedia/old_files/data/C027/C.0207640 Cylindrical measure
...sure in measure theory on topological vector spaces is a finitely-additive measure $ \mu $
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$#C+1 = 45 : ~/encyclopedia/old_files/data/G045/G.0405230 Group algebra of a locally compact group
A topological algebra with [[Involution|involution]] formed by certain functions on the group wit
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...logical group|topological group]] whose left-invariant [[Haar measure|Haar measure]] is right invariant (equivalently, is invariant under the transformation $
...athfrak{g}$), where $\mathrm{ad}$ is the adjoint representation of the Lie algebra $\mathfrak{g}$ of $G$. Any compact, discrete or Abelian locally compact gro
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...1 = 6 : ~/encyclopedia/old_files/data/H110/H.1100410 Hypergroups, harmonic analysis on locally compact
...monic analysis|Harmonic analysis]]; [[Harmonic analysis, abstract|Harmonic analysis, abstract]]; for the notion of a hypergroup, see also [[Generalized displac
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...on [[#References|[a1]]] to characterize the interpolating sequences in the algebra $H ^ { \infty }$ of bounded analytic functions in the open unit disc and to
...{D} = \{ z \in \mathbf{C} : | z | < 1 \}$. Then $\mu$ is called a Carleson measure if there exists a constant $C$ such that $\mu ( S ) \leq C h$ for every sec
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...and most important case of a product of spaces, see the article [[Measure|Measure]]. A more general construction is given below. Let $ I $
algebra $ S _ {i} $
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...nn, H. Lebesgue, M. Plancherel, L. Fejér, and F. Riesz formulated harmonic analysis as an independent mathematical discipline.
...he problem of the natural limits of the main results of classical harmonic analysis. This problem is based on the following interpretation of an ordinary Fouri
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...of locally compact groups (cf. also [[Harmonic analysis, abstract|Harmonic analysis, abstract]]). They play an important role in the duality theories of these
==Fourier–Stieltjes algebra.==
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...hfrak { g } \rightarrow \mathfrak { g }$, gives an automorphism of the Lie algebra $\frak g$. The resulting linear representation $\operatorname{Ad} : G \righ
...atorname{Aut} ( \mathfrak{g} )$, the group of all automorphisms of the Lie algebra $\frak g$.
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...( x ) ) ^ { 1 / p }$, where $m$ is some left-invariant [[Haar measure|Haar measure]] on $G$. Let $A _ { p } ( G )$ denote the set of all $u \in {\bf C} ^ { G
...y Abelian, $A _ { 2 } ( G )$ is precisely the [[Fourier-algebra(2)|Fourier algebra]] of $G$.
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$#C+1 = 41 : ~/encyclopedia/old_files/data/M063/M.0603250 Measure in a topological vector space
...gical vector space is that of extending a [[Pre-measure|pre-measure]] to a measure. Let $ E $
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of positive measure, $ \mathop{\rm mes} E > 0 $,
is a complex Borel measure on the unit circle $ \Gamma $
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be the Newton potential of a measure $ \mu \geq 0 $
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does not contain the support of a measure orthogonal to the polynomials. This condition holds if and only if for any
...of operators adjoint to the operators of multiplication by elements of the algebra.
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...additive set functions (cf. also [[Set function|Set function]]; [[Measure|Measure]]) or, more general, concerning finite additive set functions. The pioneer
...ple way. For a fixed set $A$ from a $\sigma$-algebra $\Sigma$, a classical measure $\mu : \Sigma \rightarrow [ 0 , + \infty ]$ gives that for every set $B$ fr
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algebra $ \overline {\mathcal B} \; $
if for any finite measure $ \mu $
7 KB (1,047 words) - 19:38, 5 June 2020