$#A+1 = 34 n = 2
$#C+1 = 34 : ~/encyclopedia/old_files/data/T092/T.0902690 Thom spectrum
3 KB (438 words) - 08:25, 6 June 2020
$#A+1 = 20 n = 0
$#C+1 = 20 : ~/encyclopedia/old_files/data/S086/S.0806600 Spectrum of an element
3 KB (528 words) - 08:22, 6 June 2020
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...t of all isolated eigenvalues with finite multiplicity. H. Weyl proved (in a special case) the following result [[#References|[a4]]], which is now commo
4 KB (564 words) - 17:00, 1 July 2020
$#A+1 = 28 n = 0
$#C+1 = 28 : ~/encyclopedia/old_files/data/L057/L.0507920 Lebesgue spectrum
3 KB (415 words) - 15:28, 28 February 2022
$#A+1 = 62 n = 0
$#C+1 = 62 : ~/encyclopedia/old_files/data/S086/S.0806610 Spectrum of an operator
5 KB (744 words) - 08:22, 6 June 2020
...ariants and spectral properties of the corresponding group (or semi-group) of unitary (isometric) shift operators:
...perator $A$ that is the infinitesimal generator of the one-parameter group of unitary operators $\{U_t\}$ (here $U_t=e^{itA}$, by Stone's theorem).
5 KB (710 words) - 12:58, 16 July 2014
Out of 27 formulas, 27 were replaced by TEX code.-->
Let $X$ be a CW-spectrum (see [[Spectrum of spaces|Spectrum of spaces]]) and consider
3 KB (432 words) - 16:46, 1 July 2020
...Open-closed set|open-and-closed subset]]s of its [[Spectrum of an operator|spectrum]] $\sigma(T)$ by the formula
...n algebras of sets is one of the basic problems in the [[spectral theory]] of linear operators.
1 KB (174 words) - 18:24, 22 April 2016
$#A+1 = 100 n = 0
$#C+1 = 100 : ~/encyclopedia/old_files/data/S110/S.1100230 Spectrum generating algebra,
12 KB (1,660 words) - 08:22, 6 June 2020
$#A+1 = 16 n = 3
$#C+1 = 16 : ~/encyclopedia/old_files/data/B110/B.1100930 Brown\ANDPeterson spectrum
4 KB (633 words) - 08:47, 26 March 2023
$#A+1 = 37 n = 1
$#C+1 = 37 : ~/encyclopedia/old_files/data/Q076/Q.0706460 Quasi\AAhdiscrete spectrum
7 KB (978 words) - 05:56, 19 March 2022
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...ces $\text{ker } T$ and $\operatorname{coker}T$ have finite dimension. For a semi-Fredholm operator $T$ one defines the index
5 KB (812 words) - 17:00, 1 July 2020
''of an element of a Banach algebra''
...ment]]). The spectral radius of an element $a$ is connected with the norms of its powers by the formula
2 KB (345 words) - 14:46, 21 August 2014
...periodic $A(t)$ and $f(t)$ have also been solved in terms of the spectrum of the monodromy operator.
...ative theory of differential equations in Banach spaces|Qualitative theory of differential equations in Banach spaces]].
1 KB (219 words) - 17:03, 12 August 2014
$#A+1 = 81 n = 2
$#C+1 = 81 : ~/encyclopedia/old_files/data/S086/S.0806620 Spectrum of spaces
9 KB (1,281 words) - 14:40, 21 March 2022
$#A+1 = 28 n = 0
The graded algebra $ A _ {p} $
4 KB (522 words) - 08:23, 6 June 2020
''spectral analysis of a time series''
...f. [[Spectral decomposition of a random function|Spectral decomposition of a random function]]).
2 KB (261 words) - 17:19, 7 February 2011
A mapping $U$ of a metric space $(X,\rho_X)$ into a metric space $(Y,\rho_Y)$ such that
...and $Y$ are real normed linear spaces, $U(X)=Y$ and $U(0)=0$, then $U$ is a linear operator.
2 KB (433 words) - 12:44, 18 August 2014
...s $ (F_{\alpha} \mid \alpha \in \mathfrak{A}) $ ($ \mathfrak{A} $ is a set of indices), i.e. elements $ F_{\alpha} \in \Phi' $ such that for any $ \phi \
...A \phi) = \lambda_{\alpha} {F_{\alpha}}(\phi), \qquad \alpha \in \mathfrak{A},
3 KB (517 words) - 00:44, 16 September 2015
$#A+1 = 34 n = 0
with a periodic function $ p ( z) $;
5 KB (759 words) - 22:10, 5 June 2020
''of a normal topological space $X$''
...e n$. If $\mathrm{locdim}(X) \le n$ for some $n$, then the local dimension of $X$ is finite, so one writes $\mathrm{locdim}(X) < \infty$ and puts
2 KB (304 words) - 21:59, 9 December 2014
$#A+1 = 119 n = 0
$#C+1 = 119 : ~/encyclopedia/old_files/data/P075/P.0705150 Projection spectrum
14 KB (2,029 words) - 19:53, 3 February 2021
...integral operator on the space of functions which are square-summable on $[a,b]$ is
A non-linear Volterra integral operator is an operator of the form
2 KB (370 words) - 19:05, 27 April 2014
...\operatorname{Hilb}(P_k^n/k)$ is in one-to-one correspondence with the set of closed subvarieties in $P_k^n$.
...ojective over $S$. The scheme $\operatorname{Hilb}(X/S)$ is the direct sum of the schemes $\operatorname{Hilb}^P(X/S)$ over all $P\in\mathbf Q(z)$. For a
3 KB (484 words) - 05:48, 17 April 2024
...operator]], then so is $B$; if $A$ and $B$ are bounded operators, then $\|A\|=\|B\|$.
...cient condition for the unitary equivalence of operators with a pure point spectrum.
3 KB (374 words) - 11:04, 22 August 2014
$#A+1 = 36 n = 0
A topological space $ M $
4 KB (616 words) - 19:33, 20 January 2021
$#A+1 = 106 n = 0
$#C+1 = 106 : ~/encyclopedia/old_files/data/M062/M.0602540 Markov spectrum problem
10 KB (1,413 words) - 07:59, 6 June 2020
...l operators is one of the few well-developed spectral theories for a class of non-self-adjoint operators. For the latter, see [[#References|[a3]]].
...r–Shaw inequality: If $T$ is a hyponormal operator (i.e. $[T^*,T]\geq 0$), of finite rational cyclicity $r(T)$, then:
6 KB (970 words) - 07:33, 18 March 2023
Out of 30 formulas, 30 were replaced by TEX code.-->
...all infinitely smooth functions with compact support in $\Omega$. This is a symmetric operator, and the associated quadratic form (with the same domain
4 KB (579 words) - 19:34, 7 February 2024
Out of 60 formulas, 60 were replaced by TEX code.-->
...]] and [[#References|[a4]]]), in studying homotopy classes of mappings out of various classifying spaces ([[#References|[a3]]], [[#References|[a10]]] and
7 KB (996 words) - 11:15, 20 January 2021
$#A+1 = 29 n = 0
A quantum-mechanical system consisting of a nucleus of mass $ M $
5 KB (757 words) - 19:32, 22 March 2024
...rom an automorphism $S$ of a [[Measure space|measure space]] $(X,\nu)$ and a measurable function $f$ (defined on $X$ and taking positive values)''
...s measure. The motion takes place in such a way that the second coordinate of $(x,s)$ increases with unit speed until it reaches the value $f(x)$, and th
2 KB (367 words) - 14:04, 30 August 2014
Out of 57 formulas, 56 were replaced by TEX code.-->
...gether with a strong excision axiom (i.e. $p : ( X , A ) \rightarrow ( X / A , * )$ induces an isomorphism in homology).
8 KB (1,134 words) - 17:46, 1 July 2020
$#A+1 = 59 n = 1
...e operator on a Hilbert space is a [[Linear operator|linear operator]] $ A $
7 KB (1,026 words) - 08:07, 6 June 2020
$#A+1 = 52 n = 0
...this family contained in such subspaces. More precisely, let $ {\mathcal A} $
9 KB (1,382 words) - 08:22, 6 June 2020
$#A+1 = 47 n = 0
''(in group theory)''
4 KB (568 words) - 14:10, 31 December 2020
$#A+1 = 125 n = 0
...the spectrum and its main parts, spectral multiplicity and the asymptotics of eigenvalues.
16 KB (2,424 words) - 08:22, 6 June 2020
$#A+1 = 52 n = 0
A mapping $ A $
4 KB (571 words) - 06:29, 30 May 2020
$#A+1 = 36 n = 0
...6 : ~/encyclopedia/old_files/data/S086/S.0806350 Spectral decomposition of a linear operator
5 KB (793 words) - 08:22, 6 June 2020
...tal in solid state quantum physics, this conjecture becomes in mathematics a problem in
[[Spectral theory|spectral theory]] for a Schrödinger operator (cf. also
8 KB (1,239 words) - 16:33, 4 December 2017
Out of 88 formulas, 84 were replaced by TEX code.-->
''BDF theory''
10 KB (1,450 words) - 17:44, 1 July 2020
$#A+1 = 24 n = 0
of a discrete-time stationary stochastic process such that 1) the first $ q $
6 KB (747 words) - 18:22, 14 January 2021
A complete sup-lattice $Q$ together with an associative product $\otimes$ sat
a \otimes \left({ \bigvee_i b_i }\right) = \bigvee_i a \otimes b_i
13 KB (2,065 words) - 18:59, 12 December 2023
$#A+1 = 98 n = 2
A [[Hilbert space with an indefinite metric|Hilbert space with an indefinite
9 KB (1,299 words) - 08:07, 6 June 2020
...tive group scheme is a group scheme $G$ over a basis scheme $S$, the value of which on any
...tori]]. A generalization of algebraic tori in the framework of the theory of group schemes is the following
4 KB (629 words) - 20:08, 15 December 2020
$#A+1 = 33 n = 0
+ ( a + b \cos 2z) u = 0,\ \
5 KB (803 words) - 07:59, 6 June 2020
$#A+1 = 13 n = 0
A [[Linear operator|linear operator]] $ U $
2 KB (255 words) - 08:27, 6 June 2020
$#A+1 = 32 n = 6
...ce and one time dimension [[#References|[a11]]]. It is defined in terms of a two-component quantized fermion field $ \Psi _ {k} ( x,t ) $(
8 KB (1,151 words) - 17:23, 12 May 2024
Out of 73 formulas, 72 were replaced by TEX code.-->
...and with spectral lines present in the light originating in a distant part of the Universe.
9 KB (1,326 words) - 07:37, 24 November 2023
$#A+1 = 91 n = 0
...of a certain function algebra $ A $ (cf. [[Algebra of functions|Algebra of functions]]) into the algebra $ L ( X) $
11 KB (1,521 words) - 02:23, 16 June 2022